题目传送门：http://www.lydsy.com/JudgeOnline/problem.php?id=4517
这个题目，唯一的问题在于求一个网上被称为错排的玩意
网上好像都是从实际含义来推的错排的公式
我来撸一发容斥的推法：
\(
\begin{array}{l}
f(n) = n! – C_n^1 \cdot (n – 1)! + C_n^2 \cdot (n – 2)! – \cdots – C_n^n \cdot 1!\\
f(n) = \frac{{n!}}{{2!}} – \cdots – \frac{{n!}}{{n!}}\\
f(n) = n! \cdot \sum\limits_{i = 2}^n {\frac{{{{( – 1)}^i}}}{{i!}}} \\
f(n) = f(n – 1) \cdot \frac{{n!}}{{(n – 1)!}} + {( – 1)^n}
\end{array}
\)
#include<bits/stdc++.h>
#define LL long long
using namespace std;
const int N = 1000000+9;
const int MX = 1000000;
const int MOD = 1000000007;
int p[N],d[N],REV[N];
inline int pow(int w, int t){
int ret = 1; while (t) {
if (t & 1) ret = (LL)ret * w % MOD;
w = (LL)w * w % MOD, t >>= 1;
} return ret;
}
inline LL C(int a, int b) {
return (((LL)p[a]*REV[b])%MOD)*REV[a-b] % MOD;
}
inline int read(){
char c=getchar(); int ret=0,f=1;
while (c<'0'||c>'9') {if(c=='-')f=-1;c=getchar();}
while (c<='9'&&c>='0') {ret=ret*10+c-'0';c=getchar();}
return ret*f;
}
int main(){
p[1] = p[0] = REV[0] = 1; d[1] = 0; d[0] = 1;
for (int i=2;i<=MX;i++) p[i] = (LL)p[i-1]*i % MOD;
REV[MX] = pow(p[MX],MOD-2);
for (int i=MX-1;i;i--) REV[i] = (LL)REV[i+1]*(i+1) % MOD;
for (int i=2;i<=MX;i++) d[i] = ((d[i-1] + (i&1?-REV[i]:REV[i])) % MOD + MOD) % MOD;
for (int i=0;i<=MX;i++) d[i] = (LL)d[i]*p[i] % MOD;
for (int T=read(),n,m;T;T--) {
n = read(); m = read();
if (m > n) puts("0");
else cout<<C(n,m)*d[n-m]%MOD<<endl;
} return 0;
}
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