Almost Identity Permutations

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。

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 $ .

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

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

4 1

1

4 2

7

5 3

31

5 4

76