D - Almost Identity Permutations /* Codeforces Round 888 D */

D. Almost Identity Permutations

 

Description

    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.

Input

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

Output

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

Examples

Input

4 1

Output

1

Input

4 2

Output

7

Input

5 3

Output

31

Input

5 4

Output

76

题意：
    就是有一个集合里面是1~n个元素，但是这些元素的排列是随机的。问最多有多少个这样的排列，使得至少有n-k个 pi=i。
代码：（？？？？）

#include<bits/stdc++.h>
using namespace std;
int main()
{
////先交一发别人的代码回头研究  = = 这个规律很膨胀啊 ！！！
    long long n,k,ar=1;
    cin>>n>>k;
    if(k>=2) ar+=n*(n-1)/2;
    if(k>=3) ar+=n*(n-1)*(n-2)/3;
    if(k>=4) ar+=n*(n-1)*(n-2)*(n-3)*3/8;
    cout<<ar;
    return 0;
}