uvalive 5092 - Permutation Counting

Given a permutation a1, a2, … aN of {1, 2, … , N}, we define its E-value as the amount of elements
where ai > i. For example, the E-value of permutation {1, 3, 2, 4} is 1, while the E-value of {4, 3, 2, 1}
is 2. You are requested to find how many permutations of {1, 2, … , N} whose E-value is exactly k.
Input
There are several test cases, and one line for each case, which contains two integers, N and k. (1 ≤
N ≤ 1000, 0 ≤ k ≤ N).
Output
Output one line for each case. For the answer may be quite huge, you need to output the answer module
1,000,000,007.
Explanation for the sample:
There is only one permutation with E-value 0: {1, 2, 3}, and there are four permutations with
E-value 1: {1, 3, 2}, {2, 1, 3}, {3, 1, 2}, {3, 2, 1}
Sample Input
3 0
3 1
Sample Output
1
4
规律 递推出答案

#include<stdio.h>#include<algorithm>#include<math.h>#define mod 1000000007using namespace std;//dituilong long  a[1003][1003];int main(){    for(int i=1; i<1002; i++)    {        a[i][0]=1;        for(int j=1; j<=i; j++)        {            a[i][j]=((1+j)*a[i-1][j]+(i-j)*a[i-1][j-1])%mod;        }    }    int n,k;    while(~scanf("%d%d",&n,&k))        printf("%lld\n",a[n][k]);}