Templates - number of combinations

Generally only need to use a number of combinations, and when n is greater than m MOD may find this:

const ll MOD = 1e9 + 7;
const int MAXN = 1e6;

ll inv[MAXN + 5], fac[MAXN + 5], invfac[MAXN + 5];

void init_C(int n) {
    inv[1] = 1;
    for(int i = 2; i <= n; i++)
        inv[i] = inv[MOD % i] * (MOD - MOD / i) % MOD;
    fac[0] = 1, invfac[0] = 1;
    for(int i = 1; i <= n; i++) {
        fac[i] = fac[i - 1] * i % MOD;
        invfac[i] = invfac[i - 1] * inv[i] % MOD;
    }
}

inline ll C(ll n, ll m) {
    if(n < m)
        return 0;
    return fac[n] * invfac[n - m] % MOD * invfac[m] % MOD;
}

Derangement, D [i] denotes the i-th number of kinds (different) not all the elements should be in position (ascending / descending uniquely specify a position and the like) can find out by DP, it is easy to copy the template.

const ll MOD = 1e9 + 7;
const int MAXN = 1e6;

//特殊定义D[0]为1
D[0] = 1, D[1] = 0;
for(int i = 2; i <= MAXN; i++) {
    if(i & 1) {
        D[i] = ((ll)i * D[i - 1] - 1ll) % MOD;
        if(D[i] < 0)
            D[i] += MOD;
    } else
        D[i] = ((ll)i * D[i - 1] + 1ll) % MOD;
}