This documentation is automatically generated by competitive-verifier/competitive-verifier
// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/sqrt_mod
#include "../../template/template.hpp"
#include "../../math/combinatorics/mod-pow.hpp"
#include "../../math/combinatorics/mod-sqrt.hpp"
int main() {
int T;
cin >> T;
while(T--) {
int64_t Y, P;
cin >> Y >> P;
cout << mod_sqrt(Y, P) << endl;
}
}
#line 1 "test/verify/yosupo-sqrt-mod.test.cpp"
// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/sqrt_mod
#line 1 "template/template.hpp"
#include <bits/stdc++.h>
#if __has_include(<atcoder/all>)
#include <atcoder/all>
#endif
using namespace std;
using int64 = long long;
const int64 infll = (1LL << 62) - 1;
const int inf = (1 << 30) - 1;
struct IoSetup {
IoSetup() {
cin.tie(nullptr);
ios::sync_with_stdio(false);
cout << fixed << setprecision(10);
cerr << fixed << setprecision(10);
}
} iosetup;
template <typename T1, typename T2>
ostream &operator<<(ostream &os, const pair<T1, T2> &p) {
os << p.first << " " << p.second;
return os;
}
template <typename T1, typename T2>
istream &operator>>(istream &is, pair<T1, T2> &p) {
is >> p.first >> p.second;
return is;
}
template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
for (int i = 0; i < (int)v.size(); i++) {
os << v[i] << (i + 1 != v.size() ? " " : "");
}
return os;
}
template <typename T>
istream &operator>>(istream &is, vector<T> &v) {
for (T &in : v) is >> in;
return is;
}
template <typename T1, typename T2>
inline bool chmax(T1 &a, T2 b) {
return a < b && (a = b, true);
}
template <typename T1, typename T2>
inline bool chmin(T1 &a, T2 b) {
return a > b && (a = b, true);
}
template <typename T = int64>
vector<T> make_v(size_t a) {
return vector<T>(a);
}
template <typename T, typename... Ts>
auto make_v(size_t a, Ts... ts) {
return vector<decltype(make_v<T>(ts...))>(a, make_v<T>(ts...));
}
template <typename T, typename V>
typename enable_if<is_class<T>::value == 0>::type fill_v(T &t, const V &v) {
t = v;
}
template <typename T, typename V>
typename enable_if<is_class<T>::value != 0>::type fill_v(T &t, const V &v) {
for (auto &e : t) fill_v(e, v);
}
template <typename F>
struct FixPoint : F {
explicit FixPoint(F &&f) : F(std::forward<F>(f)) {}
template <typename... Args>
decltype(auto) operator()(Args &&...args) const {
return F::operator()(*this, std::forward<Args>(args)...);
}
};
template <typename F>
inline decltype(auto) MFP(F &&f) {
return FixPoint<F>{std::forward<F>(f)};
}
#line 4 "test/verify/yosupo-sqrt-mod.test.cpp"
#line 1 "math/combinatorics/mod-pow.hpp"
/**
* @brief Mod Pow(べき乗)
*
*/
template <typename T>
T mod_pow(T x, int64_t n, const T &p) {
T ret = 1;
while (n > 0) {
if (n & 1) (ret *= x) %= p;
(x *= x) %= p;
n >>= 1;
}
return ret % p;
}
#line 1 "math/combinatorics/mod-sqrt.hpp"
/**
* @brief Mod Sqrt
*/
template <typename T>
T mod_sqrt(const T &a, const T &p) {
if (a == 0) return 0;
if (p == 2) return a;
if (mod_pow(a, (p - 1) >> 1, p) != 1) return -1;
T b = 1;
while (mod_pow(b, (p - 1) >> 1, p) == 1) ++b;
T e = 0, m = p - 1;
while (m % 2 == 0) m >>= 1, ++e;
T x = mod_pow(a, (m - 1) >> 1, p);
T y = a * (x * x % p) % p;
(x *= a) %= p;
T z = mod_pow(b, m, p);
while (y != 1) {
T j = 0, t = y;
while (t != 1) {
j += 1;
(t *= t) %= p;
}
z = mod_pow(z, T(1) << (e - j - 1), p);
(x *= z) %= p;
(z *= z) %= p;
(y *= z) %= p;
e = j;
}
return x;
}
#line 7 "test/verify/yosupo-sqrt-mod.test.cpp"
int main() {
int T;
cin >> T;
while(T--) {
int64_t Y, P;
cin >> Y >> P;
cout << mod_sqrt(Y, P) << endl;
}
}
Env | Name | Status | Elapsed | Memory |
---|---|---|---|---|
g++ | example_00 | AC | 6 ms | 3 MB |
g++ | max_random_00 | AC | 148 ms | 3 MB |
g++ | max_random_01 | AC | 147 ms | 3 MB |
g++ | max_random_02 | AC | 136 ms | 3 MB |
g++ | max_random_03 | AC | 151 ms | 3 MB |
g++ | max_random_04 | AC | 147 ms | 3 MB |
g++ | mod_998244353_00 | AC | 239 ms | 3 MB |
g++ | mod_998244353_01 | AC | 209 ms | 3 MB |
g++ | random_00 | AC | 29 ms | 3 MB |
g++ | random_01 | AC | 36 ms | 3 MB |
g++ | random_02 | AC | 109 ms | 3 MB |
g++ | random_03 | AC | 40 ms | 3 MB |
g++ | random_04 | AC | 134 ms | 3 MB |
clang++ | example_00 | AC | 5 ms | 3 MB |
clang++ | max_random_00 | AC | 135 ms | 3 MB |
clang++ | max_random_01 | AC | 155 ms | 3 MB |
clang++ | max_random_02 | AC | 152 ms | 3 MB |
clang++ | max_random_03 | AC | 138 ms | 3 MB |
clang++ | max_random_04 | AC | 147 ms | 3 MB |
clang++ | mod_998244353_00 | AC | 182 ms | 3 MB |
clang++ | mod_998244353_01 | AC | 189 ms | 3 MB |
clang++ | random_00 | AC | 34 ms | 3 MB |
clang++ | random_01 | AC | 36 ms | 3 MB |
clang++ | random_02 | AC | 97 ms | 3 MB |
clang++ | random_03 | AC | 49 ms | 3 MB |
clang++ | random_04 | AC | 175 ms | 3 MB |