Fu_L's Library

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:heavy_check_mark: verify/library_checker/enumerative_combinatrics/binomial_coefficient_prime_mod.test.cpp

Depends on

Code

#define PROBLEM "https://judge.yosupo.jp/problem/binomial_coefficient_prime_mod"
#include "../../../src/template/template.hpp"
#include "../../../src/template/dynamic_modint.hpp"
#include "../../../src/math/binomial.hpp"
using mint = modint;
int main(void) {
    int t, m;
    cin >> t >> m;
    mint::set_mod(m);
    Binomial<mint> binom(min(m - 1, 10000005));
    while(t--) {
        int n, k;
        cin >> n >> k;
        cout << binom(n, k) << '\n';
    }
}
#line 1 "verify/library_checker/enumerative_combinatrics/binomial_coefficient_prime_mod.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/binomial_coefficient_prime_mod"
#line 2 "src/template/template.hpp"
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using P = pair<long long, long long>;
#define rep(i, a, b) for(long long i = (a); i < (b); ++i)
#define rrep(i, a, b) for(long long i = (a); i >= (b); --i)
constexpr long long inf = 4e18;
struct SetupIO {
    SetupIO() {
        ios::sync_with_stdio(0);
        cin.tie(0);
        cout << fixed << setprecision(30);
    }
} setup_io;
#line 3 "src/template/dynamic_modint.hpp"
struct Barrett {
    explicit Barrett(const unsigned int m)
        : _m(m), im((unsigned long long)(-1) / m + 1) {}
    inline unsigned int umod() const {
        return _m;
    }
    inline unsigned int mul(const unsigned int a, const unsigned int b) const {
        unsigned long long z = a;
        z *= b;
        const unsigned long long x = (unsigned long long)(((unsigned __int128)(z)*im) >> 64);
        unsigned int v = (unsigned int)(z - x * _m);
        if(_m <= v) v += _m;
        return v;
    }

   private:
    unsigned int _m;
    unsigned long long im;
};
template <int id>
struct DynamicModint {
    using mint = DynamicModint;
    static int mod() {
        return (int)bt.umod();
    }
    static void set_mod(const int m) {
        assert(1 <= m);
        bt = Barrett(m);
    }
    static mint raw(const int v) {
        mint a;
        a._v = v;
        return a;
    }
    DynamicModint()
        : _v(0) {}
    template <class T>
    DynamicModint(const T& v) {
        static_assert(is_integral_v<T>);
        if(is_signed_v<T>) {
            long long x = (long long)(v % (long long)(umod()));
            if(x < 0) x += umod();
            _v = (unsigned int)(x);
        } else _v = (unsigned int)(v % umod());
    }
    unsigned int val() const {
        return _v;
    }
    mint& operator++() {
        ++_v;
        if(_v == umod()) _v = 0;
        return *this;
    }
    mint& operator--() {
        if(_v == 0) _v = umod();
        --_v;
        return *this;
    }
    mint operator++(int) {
        mint res = *this;
        ++*this;
        return res;
    }
    mint operator--(int) {
        mint res = *this;
        --*this;
        return res;
    }
    mint& operator+=(const mint& rhs) {
        _v += rhs._v;
        if(_v >= umod()) _v -= umod();
        return *this;
    }
    mint& operator-=(const mint& rhs) {
        _v += mod() - rhs._v;
        if(_v >= umod()) _v -= umod();
        return *this;
    }
    mint& operator*=(const mint& rhs) {
        _v = bt.mul(_v, rhs._v);
        return *this;
    }
    mint& operator/=(const mint& rhs) {
        return *this *= rhs.inv();
    }
    mint operator+() const {
        return *this;
    }
    mint operator-() const {
        return mint() - *this;
    }
    mint pow(long long n) const {
        assert(0 <= n);
        if(n == 0) return 1;
        mint x = *this, r = 1;
        while(1) {
            if(n & 1) r *= x;
            n >>= 1;
            if(n == 0) return r;
            x *= x;
        }
    }
    mint inv() const {
        const auto eg = inv_gcd(_v, mod());
        assert(eg.first == 1);
        return eg.second;
    }
    friend mint operator+(const mint& lhs, const mint& rhs) {
        return mint(lhs) += rhs;
    }
    friend mint operator-(const mint& lhs, const mint& rhs) {
        return mint(lhs) -= rhs;
    }
    friend mint operator*(const mint& lhs, const mint& rhs) {
        return mint(lhs) *= rhs;
    }
    friend mint operator/(const mint& lhs, const mint& rhs) {
        return mint(lhs) /= rhs;
    }
    friend bool operator==(const mint& lhs, const mint& rhs) {
        return lhs._v == rhs._v;
    }
    friend bool operator!=(const mint& lhs, const mint& rhs) {
        return lhs._v != rhs._v;
    }
    friend istream& operator>>(istream& in, mint& x) {
        long long a;
        in >> a;
        x = a;
        return in;
    }
    friend ostream& operator<<(ostream& out, const mint& x) {
        return out << x.val();
    }

   private:
    unsigned int _v = 0;
    static Barrett bt;
    inline static unsigned int umod() {
        return bt.umod();
    }
    inline static pair<long long, long long> inv_gcd(const long long a, const long long b) {
        if(a == 0) return {b, 0};
        long long s = b, t = a, m0 = 0, m1 = 1;
        while(t) {
            const long long u = s / t;
            s -= t * u;
            m0 -= m1 * u;
            swap(s, t);
            swap(m0, m1);
        }
        if(m0 < 0) m0 += b / s;
        return {s, m0};
    }
};
template <int id>
Barrett DynamicModint<id>::bt(998244353);
using modint = DynamicModint<-1>;
#line 3 "src/math/binomial.hpp"
template <typename mint>
struct Binomial {
    Binomial(int n)
        : fac(n + 1), ifac(n + 1) {
        fac[0] = 1;
        for(int i = 1; i <= n; ++i) fac[i] = fac[i - 1] * i;
        ifac[n] = fac[n].inv();
        for(int i = n; i >= 1; --i) ifac[i - 1] = ifac[i] * i;
    }
    mint fact(int n) const {
        if(n < 0) return 0;
        return fac[n];
    }
    mint perm(int n, int r) const {
        if(n < 0 or n < r or r < 0) return 0;
        return fac[n] * ifac[n - r];
    }
    mint comb(int n, int r) const {
        if(n < 0 or n < r or r < 0) return 0;
        return fac[n] * ifac[n - r] * ifac[r];
    }
    mint homo(int n, int r) const {
        if(n < 0 or r < 0) return 0;
        if(r == 0) return 1;
        return comb(n + r - 1, r);
    }
    mint operator()(int n, int r) const {
        return comb(n, r);
    }

   private:
    vector<mint> fac, ifac;
};
#line 5 "verify/library_checker/enumerative_combinatrics/binomial_coefficient_prime_mod.test.cpp"
using mint = modint;
int main(void) {
    int t, m;
    cin >> t >> m;
    mint::set_mod(m);
    Binomial<mint> binom(min(m - 1, 10000005));
    while(t--) {
        int n, k;
        cin >> n >> k;
        cout << binom(n, k) << '\n';
    }
}
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