#line 1 "verify/verify-unit-test/string-search.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/string-search.test.cpp"
//
#line 2 "string/string-search.hpp"
#line 1 "atcoder/string.hpp"
#line 9 "atcoder/string.hpp"
namespace atcoder {
namespace internal {
std::vector<int> sa_naive(const std::vector<int>& s) {
int n = int(s.size());
std::vector<int> sa(n);
std::iota(sa.begin(), sa.end(), 0);
std::sort(sa.begin(), sa.end(), [&](int l, int r) {
if (l == r) return false;
while (l < n && r < n) {
if (s[l] != s[r]) return s[l] < s[r];
l++;
r++;
}
return l == n;
});
return sa;
}
std::vector<int> sa_doubling(const std::vector<int>& s) {
int n = int(s.size());
std::vector<int> sa(n), rnk = s, tmp(n);
std::iota(sa.begin(), sa.end(), 0);
for (int k = 1; k < n; k *= 2) {
auto cmp = [&](int x, int y) {
if (rnk[x] != rnk[y]) return rnk[x] < rnk[y];
int rx = x + k < n ? rnk[x + k] : -1;
int ry = y + k < n ? rnk[y + k] : -1;
return rx < ry;
};
std::sort(sa.begin(), sa.end(), cmp);
tmp[sa[0]] = 0;
for (int i = 1; i < n; i++) {
tmp[sa[i]] = tmp[sa[i - 1]] + (cmp(sa[i - 1], sa[i]) ? 1 : 0);
}
std::swap(tmp, rnk);
}
return sa;
}
// SA-IS, linear-time suffix array construction
// Reference:
// G. Nong, S. Zhang, and W. H. Chan,
// Two Efficient Algorithms for Linear Time Suffix Array Construction
template <int THRESHOLD_NAIVE = 10, int THRESHOLD_DOUBLING = 40>
std::vector<int> sa_is(const std::vector<int>& s, int upper) {
int n = int(s.size());
if (n == 0) return {};
if (n == 1) return {0};
if (n == 2) {
if (s[0] < s[1]) {
return {0, 1};
} else {
return {1, 0};
}
}
if (n < THRESHOLD_NAIVE) {
return sa_naive(s);
}
if (n < THRESHOLD_DOUBLING) {
return sa_doubling(s);
}
std::vector<int> sa(n);
std::vector<bool> ls(n);
for (int i = n - 2; i >= 0; i--) {
ls[i] = (s[i] == s[i + 1]) ? ls[i + 1] : (s[i] < s[i + 1]);
}
std::vector<int> sum_l(upper + 1), sum_s(upper + 1);
for (int i = 0; i < n; i++) {
if (!ls[i]) {
sum_s[s[i]]++;
} else {
sum_l[s[i] + 1]++;
}
}
for (int i = 0; i <= upper; i++) {
sum_s[i] += sum_l[i];
if (i < upper) sum_l[i + 1] += sum_s[i];
}
auto induce = [&](const std::vector<int>& lms) {
std::fill(sa.begin(), sa.end(), -1);
std::vector<int> buf(upper + 1);
std::copy(sum_s.begin(), sum_s.end(), buf.begin());
for (auto d : lms) {
if (d == n) continue;
sa[buf[s[d]]++] = d;
}
std::copy(sum_l.begin(), sum_l.end(), buf.begin());
sa[buf[s[n - 1]]++] = n - 1;
for (int i = 0; i < n; i++) {
int v = sa[i];
if (v >= 1 && !ls[v - 1]) {
sa[buf[s[v - 1]]++] = v - 1;
}
}
std::copy(sum_l.begin(), sum_l.end(), buf.begin());
for (int i = n - 1; i >= 0; i--) {
int v = sa[i];
if (v >= 1 && ls[v - 1]) {
sa[--buf[s[v - 1] + 1]] = v - 1;
}
}
};
std::vector<int> lms_map(n + 1, -1);
int m = 0;
for (int i = 1; i < n; i++) {
if (!ls[i - 1] && ls[i]) {
lms_map[i] = m++;
}
}
std::vector<int> lms;
lms.reserve(m);
for (int i = 1; i < n; i++) {
if (!ls[i - 1] && ls[i]) {
lms.push_back(i);
}
}
induce(lms);
if (m) {
std::vector<int> sorted_lms;
sorted_lms.reserve(m);
for (int v : sa) {
if (lms_map[v] != -1) sorted_lms.push_back(v);
}
std::vector<int> rec_s(m);
int rec_upper = 0;
rec_s[lms_map[sorted_lms[0]]] = 0;
for (int i = 1; i < m; i++) {
int l = sorted_lms[i - 1], r = sorted_lms[i];
int end_l = (lms_map[l] + 1 < m) ? lms[lms_map[l] + 1] : n;
int end_r = (lms_map[r] + 1 < m) ? lms[lms_map[r] + 1] : n;
bool same = true;
if (end_l - l != end_r - r) {
same = false;
} else {
while (l < end_l) {
if (s[l] != s[r]) {
break;
}
l++;
r++;
}
if (l == n || s[l] != s[r]) same = false;
}
if (!same) rec_upper++;
rec_s[lms_map[sorted_lms[i]]] = rec_upper;
}
auto rec_sa =
sa_is<THRESHOLD_NAIVE, THRESHOLD_DOUBLING>(rec_s, rec_upper);
for (int i = 0; i < m; i++) {
sorted_lms[i] = lms[rec_sa[i]];
}
induce(sorted_lms);
}
return sa;
}
} // namespace internal
std::vector<int> suffix_array(const std::vector<int>& s, int upper) {
assert(0 <= upper);
for (int d : s) {
assert(0 <= d && d <= upper);
}
auto sa = internal::sa_is(s, upper);
return sa;
}
template <class T> std::vector<int> suffix_array(const std::vector<T>& s) {
int n = int(s.size());
std::vector<int> idx(n);
iota(idx.begin(), idx.end(), 0);
sort(idx.begin(), idx.end(), [&](int l, int r) { return s[l] < s[r]; });
std::vector<int> s2(n);
int now = 0;
for (int i = 0; i < n; i++) {
if (i && s[idx[i - 1]] != s[idx[i]]) now++;
s2[idx[i]] = now;
}
return internal::sa_is(s2, now);
}
std::vector<int> suffix_array(const std::string& s) {
int n = int(s.size());
std::vector<int> s2(n);
for (int i = 0; i < n; i++) {
s2[i] = s[i];
}
return internal::sa_is(s2, 255);
}
// Reference:
// T. Kasai, G. Lee, H. Arimura, S. Arikawa, and K. Park,
// Linear-Time Longest-Common-Prefix Computation in Suffix Arrays and Its
// Applications
template <class T>
std::vector<int> lcp_array(const std::vector<T>& s,
const std::vector<int>& sa) {
assert(s.size() == sa.size());
int n = int(s.size());
assert(n >= 1);
std::vector<int> rnk(n);
for (int i = 0; i < n; i++) {
assert(0 <= sa[i] && sa[i] < n);
rnk[sa[i]] = i;
}
std::vector<int> lcp(n - 1);
int h = 0;
for (int i = 0; i < n; i++) {
if (h > 0) h--;
if (rnk[i] == 0) continue;
int j = sa[rnk[i] - 1];
for (; j + h < n && i + h < n; h++) {
if (s[j + h] != s[i + h]) break;
}
lcp[rnk[i] - 1] = h;
}
return lcp;
}
std::vector<int> lcp_array(const std::string& s, const std::vector<int>& sa) {
int n = int(s.size());
std::vector<int> s2(n);
for (int i = 0; i < n; i++) {
s2[i] = s[i];
}
return lcp_array(s2, sa);
}
// Reference:
// D. Gusfield,
// Algorithms on Strings, Trees, and Sequences: Computer Science and
// Computational Biology
template <class T> std::vector<int> z_algorithm(const std::vector<T>& s) {
int n = int(s.size());
if (n == 0) return {};
std::vector<int> z(n);
z[0] = 0;
for (int i = 1, j = 0; i < n; i++) {
int& k = z[i];
k = (j + z[j] <= i) ? 0 : std::min(j + z[j] - i, z[i - j]);
while (i + k < n && s[k] == s[i + k]) k++;
if (j + z[j] < i + z[i]) j = i;
}
z[0] = n;
return z;
}
std::vector<int> z_algorithm(const std::string& s) {
int n = int(s.size());
std::vector<int> s2(n);
for (int i = 0; i < n; i++) {
s2[i] = s[i];
}
return z_algorithm(s2);
}
} // namespace atcoder
#line 2 "data-structure/sparse-table.hpp"
#line 6 "data-structure/sparse-table.hpp"
using namespace std;
template <typename T>
struct SparseTable {
inline static constexpr T INF = numeric_limits<T>::max() / 2;
int N;
vector<vector<T> > table;
T f(T a, T b) { return min(a, b); }
SparseTable() {}
SparseTable(const vector<T> &v) : N(v.size()) {
int b = 1;
while ((1 << b) <= N) ++b;
table.push_back(v);
for (int i = 1; i < b; i++) {
table.push_back(vector<T>(N, INF));
for (int j = 0; j + (1 << i) <= N; j++) {
table[i][j] = f(table[i - 1][j], table[i - 1][j + (1 << (i - 1))]);
}
}
}
// [l, r)
T query(int l, int r) {
assert(0 <= l and l <= r and r <= N);
if (l == r) return INF;
int b = 31 - __builtin_clz(r - l);
return f(table[b][l], table[b][r - (1 << b)]);
}
};
/**
* @brief Sparse Table
*/
#line 5 "string/string-search.hpp"
template <typename Container>
struct StringSearch {
const Container& S;
int N;
vector<int> sa, la, invsa;
SparseTable<int> sparse;
StringSearch(const Container& _s) : S(_s), N(S.size()) {
sa = atcoder::suffix_array(S);
la = atcoder::lcp_array(S, sa);
invsa.resize(N);
for (int i = 0; i < N; i++) invsa[sa[i]] = i;
sparse = SparseTable<int>{la};
}
// lcp(s[i, N), s[j, N))
int lcp(int i, int j) {
assert(0 <= min(i, j) and max(i, j) < N);
if (i == j) return N - i;
int x = min(invsa[i], invsa[j]);
int y = max(invsa[i], invsa[j]);
return sparse.query(x, y);
}
// lcp(s[a, b), s[c, d))
int lcp(int a, int b, int c, int d) {
assert(0 <= a and a <= b and b <= N);
assert(0 <= c and c <= d and d <= N);
int l = lcp(a, c);
return min({l, b - a, d - c});
}
// lcp(s[a, b), s[c, d))
template <typename Int>
int lcp(pair<Int, Int> p, pair<Int, Int> q) {
return lcp(p.first, p.second, q.first, q.second);
}
// s[i, N) > s[j, N) : 1
// s[i, N) = s[j, N) : 0
// s[i, N) < s[j, N) : -1
int strcmp(int i, int j) {
assert(0 <= min(i, j) and max(i, j) < N);
if (i == j) return 0;
return invsa[i] < invsa[j] ? -1 : 1;
}
// s[a, b) > s[c, d) : 1
// s[a, b) = s[c, d) : 0
// s[a, b) < s[c, d) : -1
int strcmp(int a, int b, int c, int d) {
int l = lcp(a, b, c, d);
return a + l == b ? (c + l == d ? 0 : -1)
: c + l == d ? 1
: S[a + l] < S[c + l] ? -1
: 1;
}
// s[a, b) > s[c, d) : 1
// s[a, b) = s[c, d) : 0
// s[a, b) < s[c, d) : -1
template <typename Int>
int strcmp(pair<Int, Int> p, pair<Int, Int> q) {
return strcmp(p.first, p.second, q.first, q.second);
}
};
#line 6 "verify/verify-unit-test/string-search.test.cpp"
//
#line 2 "string/rolling-hash.hpp"
#line 5 "string/rolling-hash.hpp"
using namespace std;
#line 2 "internal/internal-hash.hpp"
namespace nyaan_internal {
using i64 = long long;
using u64 = unsigned long long;
using u128 = __uint128_t;
template <int BASE_NUM = 2>
struct Hash : array<u64, BASE_NUM> {
using array<u64, BASE_NUM>::operator[];
static constexpr int n = BASE_NUM;
Hash() : array<u64, BASE_NUM>() {}
static constexpr u64 md = (1ull << 61) - 1;
constexpr static Hash set(const i64 &a) {
Hash res;
fill(begin(res), end(res), cast(a));
return res;
}
Hash &operator+=(const Hash &r) {
for (int i = 0; i < n; i++)
if (((*this)[i] += r[i]) >= md) (*this)[i] -= md;
return *this;
}
Hash &operator+=(const i64 &r) {
u64 s = cast(r);
for (int i = 0; i < n; i++)
if (((*this)[i] += s) >= md) (*this)[i] -= md;
return *this;
}
Hash &operator-=(const Hash &r) {
for (int i = 0; i < n; i++)
if (((*this)[i] += md - r[i]) >= md) (*this)[i] -= md;
return *this;
}
Hash &operator-=(const i64 &r) {
u64 s = cast(r);
for (int i = 0; i < n; i++)
if (((*this)[i] += md - s) >= md) (*this)[i] -= md;
return *this;
}
Hash &operator*=(const Hash &r) {
for (int i = 0; i < n; i++) (*this)[i] = modmul((*this)[i], r[i]);
return *this;
}
Hash &operator*=(const i64 &r) {
u64 s = cast(r);
for (int i = 0; i < n; i++) (*this)[i] = modmul((*this)[i], s);
return *this;
}
Hash operator+(const Hash &r) { return Hash(*this) += r; }
Hash operator+(const i64 &r) { return Hash(*this) += r; }
Hash operator-(const Hash &r) { return Hash(*this) -= r; }
Hash operator-(const i64 &r) { return Hash(*this) -= r; }
Hash operator*(const Hash &r) { return Hash(*this) *= r; }
Hash operator*(const i64 &r) { return Hash(*this) *= r; }
Hash operator-() const {
Hash res;
for (int i = 0; i < n; i++) res[i] = (*this)[i] == 0 ? 0 : md - (*this)[i];
return res;
}
friend Hash pfma(const Hash &a, const Hash &b, const Hash &c) {
Hash res;
for (int i = 0; i < n; i++) res[i] = modfma(a[i], b[i], c[i]);
return res;
}
friend Hash pfma(const Hash &a, const Hash &b, const i64 &c) {
Hash res;
u64 s = cast(c);
for (int i = 0; i < n; i++) res[i] = modfma(a[i], b[i], s);
return res;
}
Hash pow(long long e) {
Hash a{*this}, res{Hash::set(1)};
for (; e; a *= a, e >>= 1) {
if (e & 1) res *= a;
}
return res;
}
static Hash get_basis() {
static auto rand_time =
chrono::duration_cast<chrono::nanoseconds>(
chrono::high_resolution_clock::now().time_since_epoch())
.count();
static mt19937_64 rng(rand_time);
Hash h;
for (int i = 0; i < n; i++) {
while (isPrimitive(h[i] = rng() % (md - 1) + 1) == false)
;
}
return h;
}
private:
static u64 modpow(u64 a, u64 b) {
u64 r = 1;
for (a %= md; b; a = modmul(a, a), b >>= 1) r = modmul(r, a);
return r;
}
static bool isPrimitive(u64 x) {
for (auto &d : vector<u64>{2, 3, 5, 7, 11, 13, 31, 41, 61, 151, 331, 1321})
if (modpow(x, (md - 1) / d) <= 1) return false;
return true;
}
static inline constexpr u64 cast(const long long &a) {
return a < 0 ? a + md : a;
}
static inline constexpr u64 modmul(const u64 &a, const u64 &b) {
u128 d = u128(a) * b;
u64 ret = (u64(d) & md) + u64(d >> 61);
return ret >= md ? ret - md : ret;
}
static inline constexpr u64 modfma(const u64 &a, const u64 &b, const u64 &c) {
u128 d = u128(a) * b + c;
u64 ret = (d >> 61) + (u64(d) & md);
return ret >= md ? ret - md : ret;
}
};
} // namespace nyaan_internal
/**
* @brief ハッシュ構造体
*/
#line 8 "string/rolling-hash.hpp"
template <typename Str, int BASE_NUM = 2>
struct RollingHash {
using Hash = nyaan_internal::Hash<BASE_NUM>;
Str data;
vector<Hash> hs, pw;
int s;
static Hash basis;
RollingHash(const Str &S = Str()) { build(S); }
void build(const Str &S) {
data = S;
s = S.size();
hs.resize(s + 1);
pw.resize(s + 1);
pw[0] = Hash::set(1);
hs[0] = Hash::set(0);
for (int i = 1; i <= s; i++) {
pw[i] = pw[i - 1] * basis;
hs[i] = pfma(hs[i - 1], basis, S[i - 1]);
}
}
Hash get(int l, int r = -1) const {
if (r == -1) r = s;
return pfma(hs[l], -pw[r - l], hs[r]);
}
// T の hash を返す
static Hash get_hash(const Str &T) {
Hash ret = Hash::set(0);
for (int i = 0; i < (int)T.size(); i++) ret = pfma(ret, basis, T[i]);
return ret;
}
// a + b の hash を返す
// 引数 : a, b, b の長さ
static Hash unite(Hash a, Hash b, long long bsize) {
return pfma(a, basis.pow(bsize), b);
}
int find(Str &T, int lower = 0) const {
auto target_hash = get_hash(T);
for (int i = lower; i <= s - (int)T.size(); i++)
if (target_hash == get(i, i + (int)T.size())) return i;
return -1;
}
static int lcp(const RollingHash &a, const RollingHash &b, int al, int bl) {
int ok = 0, ng = min(a.size() - al, b.size() - bl) + 1;
while (ok + 1 < ng) {
int med = (ok + ng) / 2;
(a.get(al, med + al) == b.get(bl, med + bl) ? ok : ng) = med;
}
return ok;
}
static int strcmp(const RollingHash &a, const RollingHash &b, int al, int bl,
int ar = -1, int br = -1) {
if (ar == -1) ar = a.size();
if (br == -1) br = b.size();
int n = min<int>({lcp(a, b, al, bl), ar - al, br - bl});
return al + n == ar ? bl + n == br ? 0 : -1
: bl + n == br ? 1
: a.data[al + n] < b.data[bl + n] ? -1
: 1;
}
int size() const { return s; }
};
template <typename Str, int BASE_NUM>
typename RollingHash<Str, BASE_NUM>::Hash RollingHash<Str, BASE_NUM>::basis =
nyaan_internal::Hash<BASE_NUM>::get_basis();
using roriha = RollingHash<string, 2>;
/**
* @brief Rolling Hash
*/
#line 8 "verify/verify-unit-test/string-search.test.cpp"
//
#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 10 "verify/verify-unit-test/string-search.test.cpp"
using namespace Nyaan;
void test() {
int N = rng(5, 20);
string S;
int upper = rng(1, 10);
rep(i, N) S.push_back('a' + rng(0, upper - 1));
vp ps1;
rep(i, N) reg(j, i, N + 1) ps1.push_back({i, j});
vp ps2 = ps1;
// trc2(S);
StringSearch ss{S};
roriha rh{S};
each(p, ps1) each(q, ps1) {
string s1 = S.substr(p.fi, p.se - p.fi);
string s2 = S.substr(q.fi, q.se - q.fi);
// trc(p, q, s1, s2);
// lcp
{
int l = 0;
while (l < min(sz(s1), sz(s2)) and s1[l] == s2[l]) l++;
assert(ss.lcp(p.fi, p.se, q.fi, q.se) == l);
assert(ss.lcp(p, q) == l);
if (p.se == N and q.se == N) assert(ss.lcp(p.fi, q.fi) == l);
}
// strcmp
{
int c2 = s1 < s2 ? -1 : s1 == s2 ? 0 : 1;
int c3 = ss.strcmp(p.fi, p.se, q.fi, q.se);
int c4 = ss.strcmp(p, q);
int c5 = rh.strcmp(rh, rh, p.fi, q.fi, p.se, q.se);
assert(c2 == c3 and c3 == c4 and c4 == c5);
if (p.se == N and q.se == N) assert(ss.strcmp(p.fi, q.fi) == c2);
}
}
}
void Nyaan::solve() {
rep(t, 1000) test();
cerr << "OK" << endl;
int a, b;
cin >> a >> b;
cout << a + b << endl;
}
verify/verify-unit-test/string-search.test.cpp