math/CRT.cpp

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• Last update: 2021-09-12 23:44:25+09:00

Depends on

• math/extgcd.cpp
• template/template.cpp

Code

#pragma once
#include "../template/template.cpp"
#include "extgcd.cpp"

PL CRT(vector<ll> b, vector<ll> m) {
    ll r = 0, M = 1;
    rep(i, len(b)) {
        ll p, q;
        ll d = extGCD(M, m[i], p, q);
        if ((b[i] - r) % d) return PL(0, -1);
        ll tmp = (b[i] - r) / d * p % (m[i] / d);
        r += M * tmp;
        M *= m[i] / d;
    }
    return PL((r % M + M) % M, M);
}

#line 2 "template/template.cpp"
#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define rep(i, n) for (int i = 0; i < n; i++)
#define REP(i, n) for (int i = 1; i < n; i++)
#define rev(i, n) for (int i = n - 1; i >= 0; i--)
#define REV(i, n) for (int i = n - 1; i > 0; i--)
#define all(v) v.begin(), v.end()
#define PL pair<ll, ll>
#define PI pair<int, int>
#define pi acos(-1)
#define len(s) (int)s.size()
#define compress(v) \
    sort(all(v));   \
    v.erase(unique(all(v)), v.end());
#define comid(v, x) lower_bound(all(v), x) - v.begin()

template<class T>
using prique=priority_queue<T,vector<T>,greater<>>;

template <class T, class U>
inline bool chmin(T &a, U b) {
    if (a > b) {
        a = b;
        return true;
    }
    return false;
}
template <class T, class U>
inline bool chmax(T &a, U b) {
    if (a < b) {
        a = b;
        return true;
    }
    return false;
}
constexpr ll inf = 3e18;
#line 3 "math/extgcd.cpp"

ll extGCD(ll a, ll b, ll &x, ll &y) {
    if (!b) {
        x = 1;
        y = 0;
        return a;
    }
    ll d = extGCD(b, a % b, y, x);
    y -= a / b * x;
    return d;
}

ll modinv(ll a, ll m) {
    ll x, y;
    extGCD(a, m, x, y);
    return (x % m + m) % m;
}
#line 4 "math/CRT.cpp"

PL CRT(vector<ll> b, vector<ll> m) {
    ll r = 0, M = 1;
    rep(i, len(b)) {
        ll p, q;
        ll d = extGCD(M, m[i], p, q);
        if ((b[i] - r) % d) return PL(0, -1);
        ll tmp = (b[i] - r) / d * p % (m[i] / d);
        r += M * tmp;
        M *= m[i] / d;
    }
    return PL((r % M + M) % M, M);
}

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