卢卡斯定理

预处理阶乘。

C(n,m)%p=C(n/p,m/p)*C(n%p,m%p)%p， 即也就是Lucas(n,m)%p=Lucas(n/p,m/p)*C(n%p,m%p)%p

m! * (n - m)! 关于p的逆元就是m! * (n - m)!的p-2次方。

#include<bits/stdc++.h>
using namespace std;
using ll = long long;
constexpr int MAXN = 1000005;
constexpr int inf = 0x3f3f3f3f;
constexpr int mod = 998244353;


ll powmod(ll a, ll b, ll p) {
    ll res = 1;
    a %= p;
    while (b) {
        if (b & 1) {
            res *= a;
            res %= p;
        }
        a *= a, a %= p;
        b >>= 1;
    }
    return res;
}

ll inv(ll m, ll p) {
    return powmod(m, p - 2, p);
}
ll C(ll n, ll m, ll p) {
    if (m > n) return 0;
    ll up = 1, down = 1;
    for (int i = n - m + 1; i <= n; ++i)
        up *= i, up %= p;
    for (int i = 1; i <= m; ++i)
        down *= i, down %= p;
    return up * inv(down, p) % p;
}
ll Lucas(ll n, ll m, ll p) {
    if (m == 0) return 1;
    return C(n % p, m % p, p) * Lucas(n / p, m / p, p) % p;
}