FZU2282-组合数-逆元

题目链接

#include <iostream>
#include <queue>
#include <functional>
using namespace std;

typedef long long LL;
const int MOD = 1e9 + 7;
const int maxn = 10010;
LL pre[maxn], fac[maxn];
LL t, n, k;

void init()
{
pre[0] = 1, pre[1] = 0, pre[2] = 1;
fac[1] = 1, fac[2] = 2;
for (int i = 3; i <= 10010; i++)
{
pre[i] = (((i - 1) % MOD*(pre[i - 1] + pre[i - 2]) % MOD)) % MOD;
fac[i] = ((fac[i - 1] % MOD)*(i%MOD)) % MOD;
}
}

LL qpow(LL a, LL x) {
LL res = 1;
while (x) {
if (x & 1) {
res = (res * a) % MOD;
}
a = (a * a) % MOD;
x >>= 1;
}
return res;
}

LL C(LL n, LL k)
{
if (n < k)
return 0;
if (k > n - k)
k = n - k;
LL a = 1, b = 1;
for (int i = 0; i < k; i++)
{
a = a*(n - i) % MOD;
b = b*(i + 1) % MOD;
}
return a*qpow(b, MOD - 2) % MOD;
}
int main()
{
init();
cin >> t;
while (t--)
{
cin >> n >> k;
LL ans = 0;
for (int i = 0; i < k; i++)
{
ans = ((ans%MOD) + (C(n, i)*pre[n - i]) % MOD) % MOD;
}
cout << (MOD + (fac
% MOD) - (ans%MOD)) % MOD<<endl;
}
//system("pause");
}