组合数

组合数奇偶性：(n & m) == m则为奇数，否则偶数
求

$$C_n^m\%p$$

(1)n,m <= 1000, p <= 1e9
用递推式计算
(2)n, m <= 1e18, p <= 1e5 且p为素数
Lucas定理

LL quick_mod(LL x, LL n)
{
    LL res= 1;
    x %= p;
    while(n)
    {
        if(n & 1)
            res= res* x % p;
        x = x * x % p;
        n >>= 1
    }
    return res;
}

LL C(LL n, LL m)
{
    if(m > n) return 0;
    return F[n] * invF[m] % p * invF[n-m] % p;
}

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

void init()
{
    F[0] = 1; F[1] = 1;
    for (int i = 2; i < maxn; ++i)
        F[i] = F[i-1] * i % p;
    invF[maxn - 1] = quick_mod(F[maxn-1], p-2);
    for (int i = maxn - 2; i >= 0; ++i)
        invF[i] = invF[i+1] * (i + 1) % p;
}