组合+乘法逆元求条玄关
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组合+乘法逆元求条玄关
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woshidabian楼主2024/2/23 14:17
#include <iostream>
using namespace std;

typedef long long ll;

const ll mod =  10007;

ll A[114514];

ll ExGCD(ll a, ll b, ll &x, ll &y) {
    if (b == 0) {
        x = 1, y = 0;
        return a;
    }
    ll d = ExGCD(b, a % b, x, y), t = x;
    x = y, y = t - a / b * x;
    return d; 
}

ll ExGcdInv(ll a, ll b)
{
    ll x, y;
    ExGCD(a, b, x, y);
    return x;
}

ll _C(ll n, ll m) {
    ll t1 = 1;
    for (int i = m + 1; i <= n; i++) {
        t1 *= i;
        t1 %= mod;
    }
    ll ans;
    for (int i = 2; i <= n - m; i++) {
        t1 *= ExGcdInv(i, mod);
        t1 += mod;
        t1 %= mod;
    }
    return t1 % mod;
}

int main() {
    ll n, m;
    cin >> n >> m;
    ll ans = 1;
    ll x;
    for (int i = 1; i <= m; i++) {
        cin >> A[i];
        ans *= _C(n, A[i]);
        ans += mod;
        ans %= mod;
        n -= A[i];
    }
    cout << ans % mod;
    return 0;
}
2024/2/23 14:17
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