verify/verify-unit-test/rational-number.test.cpp

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Last update: 2026-06-27 14:52:13+09:00
Problem: https://judge.yosupo.jp/problem/aplusb

Depends on

Code

#define PROBLEM "https://judge.yosupo.jp/problem/aplusb"

#include "../../template/template.hpp"
//
#include "../../math/rational-binomial.hpp"
#include "../../math/rational-fps.hpp"
#include "../../math/rational.hpp"
//
#include "../../modint/montgomery-modint.hpp"
#include "../../modulo/binomial.hpp"
using mint = LazyMontgomeryModInt<998244353>;
//
#include "../../misc/rng.hpp"

using namespace Nyaan;

void Nyaan::solve() {
  {
    Rational a{4, 3}, b{2, 3};
    assert(a + b == 2);
    assert(a - b == Rational(2, 3));
    assert(a * b == Rational(8, 9));
    assert(a / b == 2);
    assert(a.inverse() == Rational(3, 4));
    assert(a.pow(3) == Rational(64, 27));

    assert((a > b) == true);
    assert((a >= b) == true);
    assert((a < b) == false);
    assert((a <= b) == false);
  }

  {
    Binomial_rational<Rational> C;
    assert(C.fac(3) == 6);
    assert(C.finv(3) == Rational(1, 6));
    assert(C(4, 2) == 6);
    assert(C(vi{3, 2}) == 10);
  }

  {
    using fps = FormalPowerSeries_rational<Rational>;

    {
      fps f{1, 2, {3, 2}}, g{{1, 4}, 5};
      fps h{{5, 4}, 7, {3, 2}};
      assert(f + g == h);
      h = fps{{3, 4}, -3, {3, 2}};
      assert(f - g == h);
      assert(f * g % g == fps{});
      assert(f * g % f == fps{});
    }

    {
      fps e{1, 1, {1, 2}, {1, 6}, {1, 24}, {1, 120}};
      fps f = e.pow(10);
      trc(f);
      rep(i, sz(e)) { assert(e[i] * Rational{10}.pow(i) == f[i]); }
    }
  }

  // mint と挙動の比較
  {
    auto comp = [&](int i, int j, int k, int l) {
      rep(b, 16) {
        int ii = (b >> 0) % 2 ? -i : +i;
        int jj = (b >> 1) % 2 ? -j : +j;
        int kk = (b >> 2) % 2 ? -k : +k;
        int ll = (b >> 3) % 2 ? -l : +l;
        Rational x{ii, jj}, y{kk, ll};
        mint X = mint{ii} / jj;
        mint Y = mint{kk} / ll;
        assert(X + Y == (x + y).to_mint(998244353));
        assert(X - Y == (x - y).to_mint(998244353));
        assert(X * Y == (x * y).to_mint(998244353));
        if (Y != 0) {
          assert(X / Y == (x / y).to_mint(998244353));
        }
      }
    };
    rep(i, 20) rep1(j, 20) rep(k, 20) rep1(l, 20) comp(i, j, k, l);
    rep(t, 10000) {
      int lower = t % 2 ? 1 : 32000;
      ll i = rng(lower, 35000);
      ll j = rng(lower, 35000);
      ll k = rng(lower, 35000);
      ll l = rng(lower, 35000);
      comp(i, j, k, l);
    }
  }

  // binom, mint と挙動の比較
  {
    Binomial_rational<Rational> C1;
    Binomial<mint> C2;
    reg(i, -15, 15) {
      assert(C2.fac(i) == C1.fac(i).to_mint(998244353));
      assert(C2.finv(i) == C1.finv(i).to_mint(998244353));
      assert(C2.inv(i) == C1.inv(i).to_mint(998244353));
      reg(j, -15, 15) {
        assert(C2(i, j) == C1(i, j).to_mint(998244353));
        assert(C2.P(i, j) == C1.P(i, j).to_mint(998244353));
        if (i + j < 20) assert(C2.H(i, j) == C1.H(i, j).to_mint(998244353));
      }
    }
  }

  cerr << "OK" << endl;
  {
    int s, t;
    cin >> s >> t;
    cout << s + t << "\n";
  }
}

#line 1 "verify/verify-unit-test/rational-number.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/aplusb"

#line 2 "template/template.hpp"
using namespace std;

// intrinstic
#include <immintrin.h>

#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cctype>
#include <cfenv>
#include <cfloat>
#include <chrono>
#include <cinttypes>
#include <climits>
#include <cmath>
#include <complex>
#include <cstdarg>
#include <cstddef>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <deque>
#include <fstream>
#include <functional>
#include <initializer_list>
#include <iomanip>
#include <ios>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <ostream>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <streambuf>
#include <string>
#include <tuple>
#include <type_traits>
#include <typeinfo>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

// utility
#line 3 "template/util.hpp"

namespace Nyaan {
using ll = long long;
using i64 = long long;
using u64 = unsigned long long;
using i128 = __int128_t;
using u128 = __uint128_t;

template <typename T>
using V = vector<T>;
template <typename T>
using VV = vector<vector<T>>;
using vi = vector<int>;
using vl = vector<long long>;
using vd = V<double>;
using vs = V<string>;
using vvi = vector<vector<int>>;
using vvl = vector<vector<long long>>;
template <typename T>
using minpq = priority_queue<T, vector<T>, greater<T>>;

template <typename T, typename U>
struct P : pair<T, U> {
  template <typename... Args>
  P(Args... args) : pair<T, U>(args...) {}

  using pair<T, U>::first;
  using pair<T, U>::second;

  P &operator+=(const P &r) {
    first += r.first;
    second += r.second;
    return *this;
  }
  P &operator-=(const P &r) {
    first -= r.first;
    second -= r.second;
    return *this;
  }
  P &operator*=(const P &r) {
    first *= r.first;
    second *= r.second;
    return *this;
  }
  template <typename S>
  P &operator*=(const S &r) {
    first *= r, second *= r;
    return *this;
  }
  P operator+(const P &r) const { return P(*this) += r; }
  P operator-(const P &r) const { return P(*this) -= r; }
  P operator*(const P &r) const { return P(*this) *= r; }
  template <typename S>
  P operator*(const S &r) const {
    return P(*this) *= r;
  }
  P operator-() const { return P{-first, -second}; }
};

using pl = P<ll, ll>;
using pi = P<int, int>;
using vp = V<pl>;

constexpr int inf = 1001001001;
constexpr long long infLL = 4004004004004004004LL;

template <typename T>
int sz(const T &t) {
  return t.size();
}

template <typename T, typename U>
inline bool amin(T &x, U y) {
  return (y < x) ? (x = y, true) : false;
}
template <typename T, typename U>
inline bool amax(T &x, U y) {
  return (x < y) ? (x = y, true) : false;
}

template <typename T>
inline T Max(const vector<T> &v) {
  return *max_element(begin(v), end(v));
}
template <typename T>
inline T Min(const vector<T> &v) {
  return *min_element(begin(v), end(v));
}
template <typename T>
inline long long Sum(const vector<T> &v) {
  return accumulate(begin(v), end(v), 0LL);
}

template <typename T>
int lb(const vector<T> &v, const T &a) {
  return lower_bound(begin(v), end(v), a) - begin(v);
}
template <typename T>
int ub(const vector<T> &v, const T &a) {
  return upper_bound(begin(v), end(v), a) - begin(v);
}

constexpr long long TEN(int n) {
  long long ret = 1, x = 10;
  for (; n; x *= x, n >>= 1) ret *= (n & 1 ? x : 1);
  return ret;
}

template <typename T, typename U>
pair<T, U> mkp(const T &t, const U &u) {
  return make_pair(t, u);
}

template <typename T>
vector<T> mkrui(const vector<T> &v, bool rev = false) {
  vector<T> ret(v.size() + 1);
  if (rev) {
    for (int i = int(v.size()) - 1; i >= 0; i--) ret[i] = v[i] + ret[i + 1];
  } else {
    for (int i = 0; i < int(v.size()); i++) ret[i + 1] = ret[i] + v[i];
  }
  return ret;
};

template <typename T>
vector<T> mkuni(const vector<T> &v) {
  vector<T> ret(v);
  sort(ret.begin(), ret.end());
  ret.erase(unique(ret.begin(), ret.end()), ret.end());
  return ret;
}

template <typename F>
vector<int> mkord(int N, F f) {
  vector<int> ord(N);
  iota(begin(ord), end(ord), 0);
  sort(begin(ord), end(ord), f);
  return ord;
}

template <typename T>
vector<int> mkinv(vector<T> &v) {
  int max_val = *max_element(begin(v), end(v));
  vector<int> inv(max_val + 1, -1);
  for (int i = 0; i < (int)v.size(); i++) inv[v[i]] = i;
  return inv;
}

vector<int> mkiota(int n) {
  vector<int> ret(n);
  iota(begin(ret), end(ret), 0);
  return ret;
}

template <typename T>
T mkrev(const T &v) {
  T w{v};
  reverse(begin(w), end(w));
  return w;
}

template <typename T>
bool nxp(T &v) {
  return next_permutation(begin(v), end(v));
}

// 返り値の型は入力の T に依存
// i 要素目 : [0, a[i])
template <typename T>
vector<vector<T>> product(const vector<T> &a) {
  vector<vector<T>> ret;
  vector<T> v;
  auto dfs = [&](auto rc, int i) -> void {
    if (i == (int)a.size()) {
      ret.push_back(v);
      return;
    }
    for (int j = 0; j < a[i]; j++) v.push_back(j), rc(rc, i + 1), v.pop_back();
  };
  dfs(dfs, 0);
  return ret;
}

// F : void(T&), mod を取る操作
// T : 整数型のときはオーバーフローに注意する
template <typename T, typename F>
T Power(T a, long long n, const T &I, F &&f) {
  static_assert(std::is_invocable_r_v<void, F &, T &>,
                "Power callback must be callable as void(T&)");
  T res = I;
  for (; n; std::invoke(f, a = a * a), n >>= 1) {
    if (n & 1) std::invoke(f, res = res * a);
  }
  return res;
}
// T : 整数型のときはオーバーフローに注意する
template <typename T>
T Power(T a, long long n, const T &I = T{1}) {
  auto no_op = [](T &) -> void {};
  return Power(a, n, I, no_op);
}

template <typename T>
T Rev(const T &v) {
  T res = v;
  reverse(begin(res), end(res));
  return res;
}

template <typename T>
vector<T> Transpose(const vector<T> &v) {
  using U = typename T::value_type;
  if(v.empty()) return {};
  int H = v.size(), W = v[0].size();
  vector res(W, T(H, U{}));
  for (int i = 0; i < H; i++) {
    for (int j = 0; j < W; j++) {
      res[j][i] = v[i][j];
    }
  }
  return res;
}

template <typename T>
vector<T> Rotate(const vector<T> &v, int clockwise = true) {
  using U = typename T::value_type;
  int H = v.size(), W = v[0].size();
  vector res(W, T(H, U{}));
  for (int i = 0; i < H; i++) {
    for (int j = 0; j < W; j++) {
      if (clockwise) {
        res[W - 1 - j][i] = v[i][j];
      } else {
        res[j][H - 1 - i] = v[i][j];
      }
    }
  }
  return res;
}

}  // namespace Nyaan
#line 58 "template/template.hpp"

// bit operation
#line 1 "template/bitop.hpp"
namespace Nyaan {
__attribute__((target("popcnt"))) inline int popcnt(const u64 &a) {
  return __builtin_popcountll(a);
}
inline int lsb(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }
inline int ctz(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }
inline int msb(const u64 &a) { return a ? 63 - __builtin_clzll(a) : -1; }
template <typename T>
inline int gbit(const T &a, int i) {
  return (a >> i) & 1;
}
template <typename T>
inline void sbit(T &a, int i, bool b) {
  if (gbit(a, i) != b) a ^= T(1) << i;
}
constexpr long long PW(int n) { return 1LL << n; }
constexpr long long MSK(int n) { return (1LL << n) - 1; }
}  // namespace Nyaan
#line 61 "template/template.hpp"

// inout
#line 1 "template/inout.hpp"
namespace Nyaan {

template <typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &p) {
  os << p.first << " " << p.second;
  return os;
}
template <typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &p) {
  is >> p.first >> p.second;
  return is;
}

template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
  int s = (int)v.size();
  for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];
  return os;
}
template <typename T>
istream &operator>>(istream &is, vector<T> &v) {
  for (auto &x : v) is >> x;
  return is;
}

istream &operator>>(istream &is, __int128_t &x) {
  string S;
  is >> S;
  x = 0;
  int flag = 0;
  for (auto &c : S) {
    if (c == '-') {
      flag = true;
      continue;
    }
    x *= 10;
    x += c - '0';
  }
  if (flag) x = -x;
  return is;
}

istream &operator>>(istream &is, __uint128_t &x) {
  string S;
  is >> S;
  x = 0;
  for (auto &c : S) {
    x *= 10;
    x += c - '0';
  }
  return is;
}

ostream &operator<<(ostream &os, __int128_t x) {
  if (x == 0) return os << 0;
  if (x < 0) os << '-', x = -x;
  string S;
  while (x) S.push_back('0' + x % 10), x /= 10;
  reverse(begin(S), end(S));
  return os << S;
}
ostream &operator<<(ostream &os, __uint128_t x) {
  if (x == 0) return os << 0;
  string S;
  while (x) S.push_back('0' + x % 10), x /= 10;
  reverse(begin(S), end(S));
  return os << S;
}

void in() {}
template <typename T, class... U>
void in(T &t, U &...u) {
  cin >> t;
  in(u...);
}

void out() { cout << "\n"; }
template <typename T, class... U, char sep = ' '>
void out(const T &t, const U &...u) {
  cout << t;
  if (sizeof...(u)) cout << sep;
  out(u...);
}

struct IoSetupNya {
  IoSetupNya() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(15);
    cerr << fixed << setprecision(7);
  }
} iosetupnya;

}  // namespace Nyaan
#line 64 "template/template.hpp"

// debug
#line 1 "template/debug.hpp"
namespace DebugImpl {

template <typename U, typename = void>
struct is_specialize : false_type {};
template <typename U>
struct is_specialize<
    U, typename conditional<false, typename U::iterator, void>::type>
    : true_type {};
template <typename U>
struct is_specialize<
    U, typename conditional<false, decltype(U::first), void>::type>
    : true_type {};
template <typename U>
struct is_specialize<U, enable_if_t<is_integral<U>::value, void>> : true_type {
};

void dump(const char& t) { cerr << t; }

void dump(const string& t) { cerr << t; }

void dump(const bool& t) { cerr << (t ? "true" : "false"); }

void dump(__int128_t t) {
  if (t == 0) cerr << 0;
  if (t < 0) cerr << '-', t = -t;
  string S;
  while (t) S.push_back('0' + t % 10), t /= 10;
  reverse(begin(S), end(S));
  cerr << S;
}

void dump(__uint128_t t) {
  if (t == 0) cerr << 0;
  string S;
  while (t) S.push_back('0' + t % 10), t /= 10;
  reverse(begin(S), end(S));
  cerr << S;
}

template <typename U,
          enable_if_t<!is_specialize<U>::value, nullptr_t> = nullptr>
void dump(const U& t) {
  cerr << t;
}

template <typename T>
void dump(const T& t, enable_if_t<is_integral<T>::value>* = nullptr) {
  string res;
  if (t == Nyaan::inf) res = "inf";
  if constexpr (is_signed<T>::value) {
    if (t == -Nyaan::inf) res = "-inf";
  }
  if constexpr (sizeof(T) == 8) {
    if (t == Nyaan::infLL) res = "inf";
    if constexpr (is_signed<T>::value) {
      if (t == -Nyaan::infLL) res = "-inf";
    }
  }
  if (res.empty()) res = to_string(t);
  cerr << res;
}

template <typename T, typename U>
void dump(const pair<T, U>&);
template <typename T>
void dump(const pair<T*, int>&);

template <typename T>
void dump(const T& t,
          enable_if_t<!is_void<typename T::iterator>::value>* = nullptr) {
  cerr << "[ ";
  for (auto it = t.begin(); it != t.end();) {
    dump(*it);
    cerr << (++it == t.end() ? "" : ", ");
  }
  cerr << " ]";
}

template <typename T, typename U>
void dump(const pair<T, U>& t) {
  cerr << "( ";
  dump(t.first);
  cerr << ", ";
  dump(t.second);
  cerr << " )";
}

template <typename T>
void dump(const pair<T*, int>& t) {
  cerr << "[ ";
  for (int i = 0; i < t.second; i++) {
    dump(t.first[i]);
    cerr << (i == t.second - 1 ? "" : ", ");
  }
  cerr << " ]";
}

void trace() { cerr << endl; }
template <typename Head, typename... Tail>
void trace(Head&& head, Tail&&... tail) {
  cerr << " ";
  dump(head);
  if (sizeof...(tail) != 0) cerr << ",";
  trace(std::forward<Tail>(tail)...);
}

}  // namespace DebugImpl

#ifdef NyaanDebug
#define trc(...)                            \
  do {                                      \
    cerr << "## " << #__VA_ARGS__ << " = "; \
    DebugImpl::trace(__VA_ARGS__);          \
  } while (0)
#else
#define trc(...) (void(0))
#endif

#ifdef NyaanLocal
#define trc2(...)                           \
  do {                                      \
    cerr << "## " << #__VA_ARGS__ << " = "; \
    DebugImpl::trace(__VA_ARGS__);          \
  } while (0)
#else
#define trc2(...) (void(0))
#endif
#line 67 "template/template.hpp"

// macro
#line 1 "template/macro.hpp"
#define each(x, v) for (auto&& x : v)
#define each2(x, y, v) for (auto&& [x, y] : v)
#define all(v) (v).begin(), (v).end()
#define rep(i, N) for (long long i = 0; i < (long long)(N); i++)
#define repr(i, N) for (long long i = (long long)(N)-1; i >= 0; i--)
#define rep1(i, N) for (long long i = 1; i <= (long long)(N); i++)
#define repr1(i, N) for (long long i = (N); (long long)(i) > 0; i--)
#define reg(i, a, b) for (long long i = (a); i < (b); i++)
#define regr(i, a, b) for (long long i = (b)-1; i >= (a); i--)
#define fi first
#define se second
#define ini(...)   \
  int __VA_ARGS__; \
  in(__VA_ARGS__)
#define inl(...)         \
  long long __VA_ARGS__; \
  in(__VA_ARGS__)
#define ins(...)      \
  string __VA_ARGS__; \
  in(__VA_ARGS__)
#define in2(s, t)                           \
  for (int i = 0; i < (int)s.size(); i++) { \
    in(s[i], t[i]);                         \
  }
#define in3(s, t, u)                        \
  for (int i = 0; i < (int)s.size(); i++) { \
    in(s[i], t[i], u[i]);                   \
  }
#define in4(s, t, u, v)                     \
  for (int i = 0; i < (int)s.size(); i++) { \
    in(s[i], t[i], u[i], v[i]);             \
  }
#define die(...)             \
  do {                       \
    Nyaan::out(__VA_ARGS__); \
    return;                  \
  } while (0)
#line 70 "template/template.hpp"

namespace Nyaan {
void solve();
}
int main() { Nyaan::solve(); }
#line 4 "verify/verify-unit-test/rational-number.test.cpp"
//
#line 2 "math/rational-binomial.hpp"

#line 2 "math/rational.hpp"

#line 6 "math/rational.hpp"
using namespace std;

#line 2 "internal/internal-type-traits.hpp"

#line 4 "internal/internal-type-traits.hpp"
using namespace std;

namespace nyaan_internal {
template <typename T>
using is_broadly_integral =
    typename conditional_t<is_integral_v<T> || is_same_v<T, __int128_t> ||
                               is_same_v<T, __uint128_t>,
                           true_type, false_type>::type;

template <typename T>
using is_broadly_signed =
    typename conditional_t<is_signed_v<T> || is_same_v<T, __int128_t>,
                           true_type, false_type>::type;

template <typename T>
using is_broadly_unsigned =
    typename conditional_t<is_unsigned_v<T> || is_same_v<T, __uint128_t>,
                           true_type, false_type>::type;

#define ENABLE_VALUE(x) \
  template <typename T> \
  constexpr bool x##_v = x<T>::value;

ENABLE_VALUE(is_broadly_integral);
ENABLE_VALUE(is_broadly_signed);
ENABLE_VALUE(is_broadly_unsigned);
#undef ENABLE_VALUE

#define ENABLE_HAS_TYPE(var)                                   \
  template <class, class = void>                               \
  struct has_##var : false_type {};                            \
  template <class T>                                           \
  struct has_##var<T, void_t<typename T::var>> : true_type {}; \
  template <class T>                                           \
  constexpr auto has_##var##_v = has_##var<T>::value;

#define ENABLE_HAS_VAR(var)                                     \
  template <class, class = void>                                \
  struct has_##var : false_type {};                             \
  template <class T>                                            \
  struct has_##var<T, void_t<decltype(T::var)>> : true_type {}; \
  template <class T>                                            \
  constexpr auto has_##var##_v = has_##var<T>::value;

}  // namespace nyaan_internal
#line 2 "math-fast/gcd.hpp"

#line 4 "math-fast/gcd.hpp"
using namespace std;

namespace BinaryGCDImpl {
using u64 = unsigned long long;
using i8 = char;

u64 binary_gcd(u64 a, u64 b) {
  if (a == 0 || b == 0) return a + b;
  i8 n = __builtin_ctzll(a);
  i8 m = __builtin_ctzll(b);
  a >>= n;
  b >>= m;
  n = min(n, m);
  while (a != b) {
    u64 d = a - b;
    i8 s = __builtin_ctzll(d);
    bool f = a > b;
    b = f ? b : a;
    a = (f ? d : -d) >> s;
  }
  return a << n;
}

using u128 = __uint128_t;
// a > 0
int ctz128(u128 a) {
  u64 lo = a & u64(-1);
  return lo ? __builtin_ctzll(lo) : 64 + __builtin_ctzll(a >> 64);
}
u128 binary_gcd128(u128 a, u128 b) {
  if (a == 0 || b == 0) return a + b;
  i8 n = ctz128(a);
  i8 m = ctz128(b);
  a >>= n;
  b >>= m;
  n = min(n, m);
  while (a != b) {
    u128 d = a - b;
    i8 s = ctz128(d);
    bool f = a > b;
    b = f ? b : a;
    a = (f ? d : -d) >> s;
  }
  return a << n;
}

}  // namespace BinaryGCDImpl

long long binary_gcd(long long a, long long b) {
  return BinaryGCDImpl::binary_gcd(abs(a), abs(b));
}
__int128_t binary_gcd128(__int128_t a, __int128_t b) {
  if (a < 0) a = -a;
  if (b < 0) b = -b;
  return BinaryGCDImpl::binary_gcd128(a, b);
}

/**
 * @brief binary GCD
 */
#line 10 "math/rational.hpp"

// T : 値, U : 比較用
template <typename T, typename U>
struct RationalBase {
  using R = RationalBase;
  using Key = T;
  T x, y;
  RationalBase() : x(0), y(1) {}
  template <typename T1>
  RationalBase(const T1& _x) : RationalBase<T, U>(_x, T1{1}) {}
  template <typename T1, typename T2>
  RationalBase(const pair<T1, T2>& _p)
      : RationalBase<T, U>(_p.first, _p.second) {}
  template <typename T1, typename T2>
  RationalBase(const T1& _x, const T2& _y) : x(_x), y(_y) {
    assert(y != 0);
    if (y == -1) x = -x, y = -y;
    if (y != 1) {
      T g;
      if constexpr (nyaan_internal::is_broadly_integral_v<T>) {
        if constexpr (sizeof(T) == 16) {
          g = binary_gcd128(x, y);
        } else {
          g = binary_gcd(x, y);
        }
      } else {
        g = gcd(x, y);
      }
      if (g != 0) x /= g, y /= g;
      if (y < 0) x = -x, y = -y;
    }
  }
  // y = 0 の代入も認める
  static R raw(T _x, T _y) {
    R r;
    r.x = _x, r.y = _y;
    return r;
  }
  friend R operator+(const R& l, const R& r) {
    if (l.y == r.y) return R{l.x + r.x, l.y};
    return R{l.x * r.y + l.y * r.x, l.y * r.y};
  }
  friend R operator-(const R& l, const R& r) {
    if (l.y == r.y) return R{l.x - r.x, l.y};
    return R{l.x * r.y - l.y * r.x, l.y * r.y};
  }
  friend R operator*(const R& l, const R& r) { return R{l.x * r.x, l.y * r.y}; }
  friend R operator/(const R& l, const R& r) { return R{l.x * r.y, l.y * r.x}; }
  R& operator+=(const R& r) { return (*this) = (*this) + r; }
  R& operator-=(const R& r) { return (*this) = (*this) - r; }
  R& operator*=(const R& r) { return (*this) = (*this) * r; }
  R& operator/=(const R& r) { return (*this) = (*this) / r; }
  R operator-() const { return raw(-x, y); }
  R inverse() const {
    assert(x != 0);
    R r = raw(y, x);
    if (r.y < 0) r.x = -r.x, r.y = -r.y;
    return r;
  }
  R pow(long long p) const {
    R res{1}, base{*this};
    while (p) {
      if (p & 1) res *= base;
      base *= base;
      p >>= 1;
    }
    return res;
  }
  friend bool operator==(const R& l, const R& r) {
    return l.x == r.x && l.y == r.y;
  };
  friend bool operator!=(const R& l, const R& r) {
    return l.x != r.x || l.y != r.y;
  };
  friend bool operator<(const R& l, const R& r) {
    return U{l.x} * r.y < U{l.y} * r.x;
  };
  friend bool operator<=(const R& l, const R& r) { return l < r || l == r; }
  friend bool operator>(const R& l, const R& r) {
    return U{l.x} * r.y > U{l.y} * r.x;
  };
  friend bool operator>=(const R& l, const R& r) { return l > r || l == r; }
  friend ostream& operator<<(ostream& os, const R& r) {
    os << r.x;
    if (r.x != 0 && r.y != 1) os << "/" << r.y;
    return os;
  }

  // T にキャストされるので T が bigint の場合は to_ll も要る
  T to_mint(T mod) const {
    assert(mod != 0);
    T a = y, b = mod, u = 1, v = 0, t;
    while (b > 0) {
      t = a / b;
      swap(a -= t * b, b);
      swap(u -= t * v, v);
    }
    return U((u % mod + mod) % mod) * x % mod;
  }
};

using Rational = RationalBase<long long, __int128_t>;
using Fraction = Rational;
#line 4 "math/rational-binomial.hpp"

template <typename R = Rational>
struct Binomial_rational {
  vector<R> fc;
  Binomial_rational(int = 0) { fc.emplace_back(1); }
  void extend() {
    int n = fc.size();
    R nxt = fc.back() * n;
    fc.push_back(nxt);
  }
  R fac(int n) {
    if (n < 0) return 0;
    while ((int)fc.size() <= n) extend();
    return fc[n];
  }
  R finv(int n) {
    if (n < 0) return 0;
    return fac(n).inverse();
  }
  R inv(int n) {
    if (n < 0) return -inv(-n);
    return R{1, max(n, 1)};
  }
  R C(int n, int r) {
    if (n < 0 or r < 0 or n < r) return R{0};
    return fac(n) * finv(n - r) * finv(r);
  }
  R operator()(int n, int r) { return C(n, r); }
  template <typename I>
  R multinomial(const vector<I>& r) {
    static_assert(is_integral<I>::value == true);
    int n = 0;
    for (auto& x : r) {
      if (x < 0) return R{0};
      n += x;
    }
    R res = fac(n);
    for (auto& x : r) res *= finv(x);
    return res;
  }

  template <typename I>
  R operator()(const vector<I>& r) {
    return multinomial(r);
  }
  
  R P(int n, int r) {
    if (n < 0 || n < r || r < 0) return R(0);
    return fac(n) * finv(n - r);
  }
  // [x^r] 1 / (1-x)^n
  R H(int n, int r) {
    if (n < 0 || r < 0) return R(0);
    return r == 0 ? 1 : C(n + r - 1, r);
  }
};
#line 2 "math/rational-fps.hpp"

#line 4 "math/rational-fps.hpp"

template <typename R = Rational>
struct FormalPowerSeries_rational : vector<R> {
  using vector<R>::vector;
  using fps = FormalPowerSeries_rational;

  fps &operator+=(const fps &r) {
    if (r.size() > this->size()) this->resize(r.size());
    for (int i = 0; i < (int)r.size(); i++) (*this)[i] += r[i];
    return *this;
  }

  fps &operator+=(const R &r) {
    if (this->empty()) this->resize(1);
    (*this)[0] += r;
    return *this;
  }

  fps &operator-=(const fps &r) {
    if (r.size() > this->size()) this->resize(r.size());
    for (int i = 0; i < (int)r.size(); i++) (*this)[i] -= r[i];
    return *this;
  }

  fps &operator-=(const R &r) {
    if (this->empty()) this->resize(1);
    (*this)[0] -= r;
    return *this;
  }

  fps &operator*=(const fps &r) {
    int n = this->size() + r.size() - 1;
    fps f(n);
    for (int i = 0; i < (int)this->size(); i++) {
      for (int j = 0; j < (int)r.size(); j++) {
        f[i + j] += (*this)[i] * r[j];
      }
    }
    return *this = f;
  }

  fps &operator*=(const R &v) {
    for (int k = 0; k < (int)this->size(); k++) (*this)[k] *= v;
    return *this;
  }

  fps &operator/=(const fps &r) {
    if (this->size() < r.size()) {
      this->clear();
      return *this;
    }
    int n = this->size() - r.size() + 1;
    fps f(*this), g(r);
    g.shrink();
    R coeff = g.back().inverse();
    for (auto &x : g) x *= coeff;
    int deg = (int)f.size() - (int)g.size() + 1;
    int gs = g.size();
    fps quo(deg);
    for (int i = deg - 1; i >= 0; i--) {
      quo[i] = f[i + gs - 1];
      for (int j = 0; j < gs; j++) f[i + j] -= quo[i] * g[j];
    }
    *this = quo * coeff;
    this->resize(n, R(0));
    return *this;
  }

  fps &operator%=(const fps &r) {
    *this -= *this / r * r;
    shrink();
    return *this;
  }

  fps operator+(const fps &r) const { return fps(*this) += r; }
  fps operator+(const R &v) const { return fps(*this) += v; }
  fps operator-(const fps &r) const { return fps(*this) -= r; }
  fps operator-(const R &v) const { return fps(*this) -= v; }
  fps operator*(const fps &r) const { return fps(*this) *= r; }
  fps operator*(const R &v) const { return fps(*this) *= v; }
  fps operator/(const fps &r) const { return fps(*this) /= r; }
  fps operator%(const fps &r) const { return fps(*this) %= r; }
  fps operator-() const {
    fps ret(this->size());
    for (int i = 0; i < (int)this->size(); i++) ret[i] = -(*this)[i];
    return ret;
  }

  void shrink() {
    while (this->size() && this->back() == R(0)) this->pop_back();
  }

  fps rev() const {
    fps ret(*this);
    reverse(begin(ret), end(ret));
    return ret;
  }

  fps dot(fps r) const {
    fps ret(min(this->size(), r.size()));
    for (int i = 0; i < (int)ret.size(); i++) ret[i] = (*this)[i] * r[i];
    return ret;
  }

  // 前 sz 項を取ってくる。sz に足りない項は 0 埋めする
  fps pre(int sz) const {
    fps ret(begin(*this), begin(*this) + min((int)this->size(), sz));
    if ((int)ret.size() < sz) ret.resize(sz);
    return ret;
  }

  fps operator>>(int sz) const {
    if ((int)this->size() <= sz) return {};
    fps ret(*this);
    ret.erase(ret.begin(), ret.begin() + sz);
    return ret;
  }

  fps operator<<(int sz) const {
    fps ret(*this);
    ret.insert(ret.begin(), sz, R(0));
    return ret;
  }

  fps diff() const {
    const int n = (int)this->size();
    fps ret(max(0, n - 1));
    R one(1), coeff(1);
    for (int i = 1; i < n; i++) {
      ret[i - 1] = (*this)[i] * coeff;
      coeff += one;
    }
    return ret;
  }

  fps integral() const {
    const int n = (int)this->size();
    fps ret(n + 1);
    for (int i = 0; i < n; i++) ret[i + 1] = (*this)[i] / (i + 1);
    return ret;
  }

  R eval(R x) const {
    R r = 0, w = 1;
    for (auto &v : *this) r += w * v, w *= x;
    return r;
  }

  fps inv(int deg = -1) const {
    assert((*this)[0] != R(0));
    if (deg == -1) deg = (*this).size();
    fps ret{R(1) / (*this)[0]};
    for (int i = 1; i < deg; i <<= 1) {
      ret = (ret + ret - ret * ret * (*this).pre(i << 1)).pre(i << 1);
    }
    return ret.pre(deg);
  }
  fps log(int deg = -1) const {
    assert(!(*this).empty() && (*this)[0] == R(1));
    if (deg == -1) deg = (int)this->size();
    return (this->diff() * this->inv(deg)).pre(deg - 1).integral();
  }
  fps exp(int deg = -1) const {
    assert((*this).size() == 0 || (*this)[0] == R(0));
    if (deg == -1) deg = (int)this->size();
    fps ret{R(1)};
    for (int i = 1; i < deg; i <<= 1) {
      ret = (ret * (pre(i << 1) + R(1) - ret.log(i << 1))).pre(i << 1);
    }
    return ret.pre(deg);
  }
  fps pow(int64_t k, int deg = -1) const {
    const int n = (int)this->size();
    if (deg == -1) deg = n;
    if (k == 0) {
      fps ret(deg);
      if (deg) ret[0] = 1;
      return ret;
    }
    for (int i = 0; i < n; i++) {
      if ((*this)[i] != R(0)) {
        R rev = R(1) / (*this)[i];
        fps ret = (((*this * rev) >> i).log(deg) * k).exp(deg);
        ret *= (*this)[i].pow(k);
        ret = (ret << (i * k)).pre(deg);
        if ((int)ret.size() < deg) ret.resize(deg, R(0));
        return ret;
      }
      if (__int128_t(i + 1) * k >= deg) return fps(deg, R(0));
    }
    return fps(deg, R(0));
  }
};
#line 8 "verify/verify-unit-test/rational-number.test.cpp"
//
#line 2 "modint/montgomery-modint.hpp"

#line 5 "modint/montgomery-modint.hpp"

template <uint32_t mod>
struct LazyMontgomeryModInt {
  using mint = LazyMontgomeryModInt;
  using i32 = int32_t;
  using u32 = uint32_t;
  using u64 = uint64_t;

  static constexpr u32 get_r() {
    u32 ret = mod;
    for (i32 i = 0; i < 4; ++i) ret *= 2 - mod * ret;
    return ret;
  }

  static constexpr u32 r = get_r();
  static constexpr u32 n2 = -u64(mod) % mod;
  static_assert(mod < (1 << 30), "invalid, mod >= 2 ^ 30");
  static_assert((mod & 1) == 1, "invalid, mod % 2 == 0");
  static_assert(r * mod == 1, "this code has bugs.");

  u32 a;

  constexpr LazyMontgomeryModInt() : a(0) {}
  constexpr LazyMontgomeryModInt(const int64_t &b)
      : a(reduce(u64(b % mod + mod) * n2)){};

  static constexpr u32 reduce(const u64 &b) {
    return (b + u64(u32(b) * u32(-r)) * mod) >> 32;
  }

  constexpr mint &operator+=(const mint &b) {
    if (i32(a += b.a - 2 * mod) < 0) a += 2 * mod;
    return *this;
  }

  constexpr mint &operator-=(const mint &b) {
    if (i32(a -= b.a) < 0) a += 2 * mod;
    return *this;
  }

  constexpr mint &operator*=(const mint &b) {
    a = reduce(u64(a) * b.a);
    return *this;
  }

  constexpr mint &operator/=(const mint &b) {
    *this *= b.inverse();
    return *this;
  }

  constexpr mint operator+(const mint &b) const { return mint(*this) += b; }
  constexpr mint operator-(const mint &b) const { return mint(*this) -= b; }
  constexpr mint operator*(const mint &b) const { return mint(*this) *= b; }
  constexpr mint operator/(const mint &b) const { return mint(*this) /= b; }
  constexpr bool operator==(const mint &b) const {
    return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a);
  }
  constexpr bool operator!=(const mint &b) const {
    return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a);
  }
  constexpr mint operator-() const { return mint() - mint(*this); }
  constexpr mint operator+() const { return mint(*this); }

  constexpr mint pow(u64 n) const {
    mint ret(1), mul(*this);
    while (n > 0) {
      if (n & 1) ret *= mul;
      mul *= mul;
      n >>= 1;
    }
    return ret;
  }

  constexpr mint inverse() const {
    int x = get(), y = mod, u = 1, v = 0, t = 0, tmp = 0;
    while (y > 0) {
      t = x / y;
      x -= t * y, u -= t * v;
      tmp = x, x = y, y = tmp;
      tmp = u, u = v, v = tmp;
    }
    return mint{u};
  }

  friend std::ostream &operator<<(std::ostream &os, const mint &b) {
    return os << b.get();
  }

  friend std::istream &operator>>(std::istream &is, mint &b) {
    int64_t t;
    is >> t;
    b = LazyMontgomeryModInt<mod>(t);
    return (is);
  }

  constexpr u32 get() const {
    u32 ret = reduce(a);
    return ret >= mod ? ret - mod : ret;
  }

  static constexpr u32 get_mod() { return mod; }
};
#line 2 "modulo/binomial.hpp"

#line 6 "modulo/binomial.hpp"
using namespace std;

// コンストラクタの MAX に 「C(n, r) や fac(n) でクエリを投げる最大の n 」
// を入れると倍速くらいになる
// mod を超えて前計算して 0 割りを踏むバグは対策済み
template <typename T>
struct Binomial {
  vector<T> f, g, h;
  Binomial(int MAX = 0) {
    assert(T::get_mod() != 0 && "Binomial<mint>()");
    f.resize(1, T{1});
    g.resize(1, T{1});
    h.resize(1, T{1});
    if (MAX > 0) extend(MAX + 1);
  }

  void extend(int m = -1) {
    int n = f.size();
    if (m == -1) m = n * 2;
    m = min<int>(m, T::get_mod());
    if (n >= m) return;
    f.resize(m);
    g.resize(m);
    h.resize(m);
    for (int i = n; i < m; i++) f[i] = f[i - 1] * T(i);
    g[m - 1] = f[m - 1].inverse();
    h[m - 1] = g[m - 1] * f[m - 2];
    for (int i = m - 2; i >= n; i--) {
      g[i] = g[i + 1] * T(i + 1);
      h[i] = g[i] * f[i - 1];
    }
  }

  T fac(int i) {
    if (i < 0) return T(0);
    while (i >= (int)f.size()) extend();
    return f[i];
  }

  T finv(int i) {
    if (i < 0) return T(0);
    while (i >= (int)g.size()) extend();
    return g[i];
  }

  T inv(int i) {
    if (i < 0) return -inv(-i);
    while (i >= (int)h.size()) extend();
    return h[i];
  }

  T C(int n, int r) {
    if (n < 0 || n < r || r < 0) return T(0);
    return fac(n) * finv(n - r) * finv(r);
  }

  inline T operator()(int n, int r) { return C(n, r); }

  template <typename I>
  T multinomial(const vector<I>& r) {
    static_assert(is_integral<I>::value == true);
    int n = 0;
    for (auto& x : r) {
      if (x < 0) return T(0);
      n += x;
    }
    T res = fac(n);
    for (auto& x : r) res *= finv(x);
    return res;
  }

  template <typename I>
  T operator()(const vector<I>& r) {
    return multinomial(r);
  }

  T C_naive(int n, int r) {
    if (n < 0 || n < r || r < 0) return T(0);
    T ret = T(1);
    r = min(r, n - r);
    for (int i = 1; i <= r; ++i) ret *= inv(i) * (n--);
    return ret;
  }

  T P(int n, int r) {
    if (n < 0 || n < r || r < 0) return T(0);
    return fac(n) * finv(n - r);
  }

  // [x^r] 1 / (1-x)^n
  T H(int n, int r) {
    if (n < 0 || r < 0) return T(0);
    return r == 0 ? 1 : C(n + r - 1, r);
  }
};
#line 11 "verify/verify-unit-test/rational-number.test.cpp"
using mint = LazyMontgomeryModInt<998244353>;
//
#line 2 "misc/rng.hpp"

#line 7 "misc/rng.hpp"
using namespace std;

#line 2 "internal/internal-seed.hpp"

#line 4 "internal/internal-seed.hpp"
using namespace std;

namespace nyaan_internal {
unsigned long long non_deterministic_seed() {
  unsigned long long m =
      chrono::duration_cast<chrono::nanoseconds>(
          chrono::high_resolution_clock::now().time_since_epoch())
          .count();
  m ^= 9845834732710364265uLL;
  m ^= m << 24, m ^= m >> 31, m ^= m << 35;
  return m;
}
unsigned long long deterministic_seed() { return 88172645463325252UL; }

// 64 bit の seed 値を生成 (手元では seed 固定)
// 連続で呼び出すと同じ値が何度も返ってくるので注意
// #define RANDOMIZED_SEED するとシードがランダムになる
unsigned long long seed() {
#if defined(NyaanLocal) && !defined(RANDOMIZED_SEED)
  return deterministic_seed();
#else
  return non_deterministic_seed();
#endif
}

}  // namespace nyaan_internal
#line 10 "misc/rng.hpp"

namespace my_rand {
using i64 = long long;
using u64 = unsigned long long;

// [0, 2^64 - 1)
u64 rng() {
  static u64 _x = nyaan_internal::seed();
  return _x ^= _x << 7, _x ^= _x >> 9;
}

// [l, r]
i64 rng(i64 l, i64 r) {
  assert(l <= r);
  return l + rng() % u64(r - l + 1);
}

// [l, r)
i64 randint(i64 l, i64 r) {
  assert(l < r);
  return l + rng() % u64(r - l);
}

// choose n numbers from [l, r) without overlapping
vector<i64> randset(i64 l, i64 r, i64 n) {
  assert(l <= r && n <= r - l);
  unordered_set<i64> s;
  for (i64 i = n; i; --i) {
    i64 m = randint(l, r + 1 - i);
    if (s.find(m) != s.end()) m = r - i;
    s.insert(m);
  }
  vector<i64> ret;
  for (auto& x : s) ret.push_back(x);
  sort(begin(ret), end(ret));
  return ret;
}

// [0.0, 1.0)
double rnd() { return rng() * 5.42101086242752217004e-20; }
// [l, r)
double rnd(double l, double r) {
  assert(l < r);
  return l + rnd() * (r - l);
}

template <typename T>
void randshf(vector<T>& v) {
  int n = v.size();
  for (int i = 1; i < n; i++) swap(v[i], v[randint(0, i + 1)]);
}

}  // namespace my_rand

using my_rand::randint;
using my_rand::randset;
using my_rand::randshf;
using my_rand::rnd;
using my_rand::rng;
#line 14 "verify/verify-unit-test/rational-number.test.cpp"

using namespace Nyaan;

void Nyaan::solve() {
  {
    Rational a{4, 3}, b{2, 3};
    assert(a + b == 2);
    assert(a - b == Rational(2, 3));
    assert(a * b == Rational(8, 9));
    assert(a / b == 2);
    assert(a.inverse() == Rational(3, 4));
    assert(a.pow(3) == Rational(64, 27));

    assert((a > b) == true);
    assert((a >= b) == true);
    assert((a < b) == false);
    assert((a <= b) == false);
  }

  {
    Binomial_rational<Rational> C;
    assert(C.fac(3) == 6);
    assert(C.finv(3) == Rational(1, 6));
    assert(C(4, 2) == 6);
    assert(C(vi{3, 2}) == 10);
  }

  {
    using fps = FormalPowerSeries_rational<Rational>;

    {
      fps f{1, 2, {3, 2}}, g{{1, 4}, 5};
      fps h{{5, 4}, 7, {3, 2}};
      assert(f + g == h);
      h = fps{{3, 4}, -3, {3, 2}};
      assert(f - g == h);
      assert(f * g % g == fps{});
      assert(f * g % f == fps{});
    }

    {
      fps e{1, 1, {1, 2}, {1, 6}, {1, 24}, {1, 120}};
      fps f = e.pow(10);
      trc(f);
      rep(i, sz(e)) { assert(e[i] * Rational{10}.pow(i) == f[i]); }
    }
  }

  // mint と挙動の比較
  {
    auto comp = [&](int i, int j, int k, int l) {
      rep(b, 16) {
        int ii = (b >> 0) % 2 ? -i : +i;
        int jj = (b >> 1) % 2 ? -j : +j;
        int kk = (b >> 2) % 2 ? -k : +k;
        int ll = (b >> 3) % 2 ? -l : +l;
        Rational x{ii, jj}, y{kk, ll};
        mint X = mint{ii} / jj;
        mint Y = mint{kk} / ll;
        assert(X + Y == (x + y).to_mint(998244353));
        assert(X - Y == (x - y).to_mint(998244353));
        assert(X * Y == (x * y).to_mint(998244353));
        if (Y != 0) {
          assert(X / Y == (x / y).to_mint(998244353));
        }
      }
    };
    rep(i, 20) rep1(j, 20) rep(k, 20) rep1(l, 20) comp(i, j, k, l);
    rep(t, 10000) {
      int lower = t % 2 ? 1 : 32000;
      ll i = rng(lower, 35000);
      ll j = rng(lower, 35000);
      ll k = rng(lower, 35000);
      ll l = rng(lower, 35000);
      comp(i, j, k, l);
    }
  }

  // binom, mint と挙動の比較
  {
    Binomial_rational<Rational> C1;
    Binomial<mint> C2;
    reg(i, -15, 15) {
      assert(C2.fac(i) == C1.fac(i).to_mint(998244353));
      assert(C2.finv(i) == C1.finv(i).to_mint(998244353));
      assert(C2.inv(i) == C1.inv(i).to_mint(998244353));
      reg(j, -15, 15) {
        assert(C2(i, j) == C1(i, j).to_mint(998244353));
        assert(C2.P(i, j) == C1.P(i, j).to_mint(998244353));
        if (i + j < 20) assert(C2.H(i, j) == C1.H(i, j).to_mint(998244353));
      }
    }
  }

  cerr << "OK" << endl;
  {
    int s, t;
    cin >> s >> t;
    cout << s + t << "\n";
  }
}

Nyaan's Library

This documentation is automatically generated by online-judge-tools/verification-helper

verify/verify-unit-test/rational-number.test.cpp

Depends on

Code