Almost Identity Permutations

题意翻译

给出n和k计算满足至少有(n-k)个位置的值a[i]==i的1~n的全排列的个数。

题目描述

A permutation $ p $ of size $ n $ is an array such that every integer from $ 1 $ to $ n $ occurs exactly once in this array. Let's call a permutation an almost identity permutation iff there exist at least $ n-k $ indices $ i $ ( $ 1<=i<=n $ ) such that $ p_{i}=i $ . Your task is to count the number of almost identity permutations for given numbers $ n $ and $ k $ .

输入输出格式

输入格式

The first line contains two integers $ n $ and $ k $ ( $ 4<=n<=1000 $ , $ 1<=k<=4 $ ).

输出格式

Print the number of almost identity permutations for given $ n $ and $ k $ .

输入输出样例

输入样例 #1

4 1

输出样例 #1

1

输入样例 #2

4 2

输出样例 #2

7

输入样例 #3

5 3

输出样例 #3

31

输入样例 #4

5 4

输出样例 #4

76