tests/Sqrt_Mod.test.cpp

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Last update: 2025-11-28 02:09:51+07:00
Problem: https://judge.yosupo.jp/problem/sqrt_mod

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Code

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

#include "../misc/macros.h"
#include "../math/ModInt.h"
#include "../math/ModSQRT.h"

void solve() {
  int y, p;
  cin >> y >> p;
  cout << modsqrt(y, p) << '\n';
}

int main() {
  cin.tie(0)->sync_with_stdio(0);
  cin.exceptions(cin.failbit);
  int tc = 1;
  cin >> tc;
  for (int i = 1; i <= tc; ++i) {
    solve();
  }
}

#line 1 "tests/Sqrt_Mod.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/sqrt_mod"

#line 1 "misc/macros.h"
// #pragma GCC optimize("Ofast,unroll-loops")       // unroll long, simple loops
// #pragma GCC target("avx2,fma")                   // vectorizing code
// #pragma GCC target("lzcnt,popcnt,abm,bmi,bmi2")  // for fast bitset operation

#include <bits/extc++.h>
#include <tr2/dynamic_bitset>

using namespace std;
using namespace __gnu_pbds;  // ordered_set, gp_hash_table
// using namespace __gnu_cxx; // rope

// for templates to work
#define all(x) (x).begin(), (x).end()
#define sz(x) (int) (x).size()
#define pb push_back
#define eb emplace_back
using i32 = int32_t;
using u32 = uint32_t;
using i64 = int64_t;
using u64 = uint64_t;
using i128 = __int128_t;
using u128 = __uint128_t;
using ld = long double;
using pii = pair<i32, i32>;
using vi = vector<i32>;

// fast map
const int RANDOM = chrono::high_resolution_clock::now().time_since_epoch().count();
struct chash {  // customize hash function for gp_hash_table
  int operator()(int x) const { return x ^ RANDOM; }
};
gp_hash_table<int, int, chash> table;

/* ordered set
    find_by_order(k): returns an iterator to the k-th element (0-based)
    order_of_key(k): returns the number of elements in the set that are strictly less than k
*/
template <class T>
using ordered_set = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;

/*  rope
    rope <int> cur = v.substr(l, r - l + 1);
    v.erase(l, r - l + 1);
    v.insert(v.mutable_begin(), cur);
*/
#line 2 "math/ModInt.h"

template <int mod>
struct modint {
  using M = modint;
  static_assert(mod > 0 && mod <= 2147483647);
  static constexpr int modulo = mod;
  static constexpr u32 r1 = []() {
    u32 r1 = mod;
    for (int i = 0; i < 5; ++i) r1 *= 2 - mod * r1;
    return -r1;
  }();
  static constexpr u32 r2 = -u64(mod) % mod;
  static u32 reduce(u64 x) {
    u32 y = u32(x) * r1, r = (x + u64(y) * mod) >> 32;
    return r >= mod ? r - mod : r;
  }
  u32 x;
  modint() : x(0) {}
  modint(i64 x) : x(reduce(u64(x % mod + mod) * r2)) {}
  M& operator+=(const M& a) {
    if ((x += a.x) >= mod) x -= mod;
    return *this;
  }
  M& operator-=(const M& a) {
    if ((x += mod - a.x) >= mod) x -= mod;
    return *this;
  }
  M& operator*=(const M& a) {
    x = reduce(u64(x) * a.x);
    return *this;
  }
  M& operator/=(const M& a) { return *this *= a.inv(); }
  M operator-() const { return M(0) - *this; }
  M operator+(const M& a) const { return M(*this) += a; }
  M operator-(const M& a) const { return M(*this) -= a; }
  M operator*(const M& a) const { return M(*this) *= a; }
  M operator/(const M& a) const { return M(*this) /= a; }
  bool operator==(const M& a) const { return x == a.x; }
  bool operator!=(const M& a) const { return x != a.x; }
  M pow(u64 k) const {
    M res(1), b = *this;
    while (k) {
      if (k & 1) res *= b;
      b *= b, k >>= 1;
    }
    return res;
  }
  M inv() const { return pow(mod - 2); }
  friend ostream& operator<<(ostream& os, const M& a) {
    return os << reduce(a.x);
  }
  friend istream& operator>>(istream& is, M& a) {
    i64 v;
    is >> v;
    a = M(v);
    return is;
  }
};

u64 modmul(u64 x, u64 y, u64 m) { return u128(x) * y % m; }
u64 modpow(u64 x, u64 k, u64 m) {
  u64 res = 1;
  while (k) {
    if (k & 1) res = modmul(res, x, m);
    x = modmul(x, x, m);
    k >>= 1;
  }
  return res;
}
#line 1 "math/ModSQRT.h"
i64 modsqrt(i64 a, i64 p) {
  a %= p;
  if (a < 0) a += p;
  if (a == 0) return 0;

  if (modpow(a, (p - 1) / 2, p) != 1) return -1;
  if (p % 4 == 3) return modpow(a, (p + 1) / 4, p);
  // a^(n+3)/8 or 2^(n+3)/8 * 2^(n-1)/4 works if p % 8 == 5
  i64 s = p - 1, n = 2;
  int r = 0, m;
  while (s % 2 == 0) ++r, s /= 2;
  /// find a non-square mod p
  while (modpow(n, (p - 1) / 2, p) != p - 1) ++n;
  i64 x = modpow(a, (s + 1) / 2, p);
  i64 b = modpow(a, s, p), g = modpow(n, s, p);
  for (;; r = m) {
    i64 t = b;
    for (m = 0; m < r && t != 1; ++m) t = t * t % p;
    if (m == 0) return x;
    i64 gs = modpow(g, 1LL << (r - m - 1), p);
    g = gs * gs % p;
    x = x * gs % p;
    b = b * g % p;
  }
}
#line 6 "tests/Sqrt_Mod.test.cpp"

void solve() {
  int y, p;
  cin >> y >> p;
  cout << modsqrt(y, p) << '\n';
}

int main() {
  cin.tie(0)->sync_with_stdio(0);
  cin.exceptions(cin.failbit);
  int tc = 1;
  cin >> tc;
  for (int i = 1; i <= tc; ++i) {
    solve();
  }
}