[BZOJ4517][SDOI2016]排列计数(错位排列)

没有任何难度的组合数水题，只要知道错排公式即可。注意$f_1=1$

$$ans=C_n^m*f_{n-m} \quad f_n=(n-1)(f_{n-1}+f_{n-2})$$

快速幂竟然会写错？

#include<cstdio>
#include<algorithm>
#define rep(i,l,r) for (ll i=(l); i<=(r); i++)
typedef long long ll;
using namespace std;

const ll N=1000000,mod=1000000007;
ll n,m,T,fin[N+10],fac[N+10],f[N+10];

ll pow(ll a,ll b){
ll res;
for (res=1; b; a=(a*a)%mod,b>>=1)
if (b & 1) res=(res*a)%mod;
return res;
}

int main(){
freopen("permutation.in","r",stdin);
freopen("permutation.out","w",stdout);
fac[0]=1; rep(i,1,N) fac[i]=(fac[i-1]*i)%mod;
fin
=pow(fac
,mod-2);
for (ll i=N-1; ~i; i--) fin[i]=(fin[i+1]*(i+1))%mod;
f[0]=1; f[1]=0; f[2]=1; rep(i,3,N) f[i]=((i-1)*(f[i-1]+f[i-2]))%mod;
for (scanf("%lld",&T); T--; )
scanf("%lld%lld",&n,&m),printf("%lld\n",((fac
*fin[m]%mod*fin[n-m])%mod*f[n-m])%mod);
return 0;
}