A11423. Almost Identity Permutations

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 $k$ .