lucas 快速求大数组合数

根据公式就是 对每次C(n,m) =  C(n%p,m%p) * C(n/p,m/p);

ll pow(ll x,ll n) {
    ll res = 1;
    x%=mod;
    while (n) {
        if(n&1) res = res*x%mod;
        x = x*x %mod;
        n >>=1;
    }
    return res;
}

ll C(ll n,ll m) {
    if(n < m) return 0;
    // c(n,m) = n!/m!/(n-m)!
    ll res = 1;
    for(int i=1; i<=m; i++) {
        ll a = (n+i-m)%mod;
        ll b = i%mod;
        res = res*(a*pow(b,mod-2)%mod)%mod;
    }
    return res;
}

ll Lucas(ll n,ll m) {
    if(m == 0) return 1;
    return C(n%mod, m%mod) * Lucas(n/mod,m/mod)%mod;
}