Little Rooks

Description

Inspired by a "Little Bishops" problem, Petya now wants to solve problem for rooks. 

A rook is a piece used in the game of chess which is played on a board of square grids. A rook can only move horizontally and vertically from its current position and two rooks attack each other if one is on the path of the other. 

Given two numbers n and k, your job is to determine the number of ways one can put k rooks on an n × n chessboard so that no two of them are in attacking positions. 

Input

The input file contains two integers n (1 ≤ n ≤ 10) and k (0 ≤ k ≤ n²). 

Output

Print a line containing the total number of ways one can put the given number of rooks on a chessboard of the given size so that no two of them are in attacking positions. 

Sample Input

Input

 

4 4 

Output

 

24 

 

根据规则，每一行只能有一个棋子，采用排列组合的话，

1.当n > k 时，为0.

2.当n = k 时，为A(n,k).

3.当k < n的时候，从n列中拿出k行，剩余n-k+1行。k行则与 n=k 时的排列时一样的，即A（n,k),将剩余的n-k+1行插入k行中，为C（n,k）。所以总的摆放数为：A（n,k)*C(n,k).

 

#include <iostream>
#include <cmath>
#include <cstring>
#include <algorithm>
using namespace std;
int main()
{
  int n,k;
  while(cin>>n>>k)
  {
     if(k > n)
       cout<<0<<endl;
    else
    {
       int sum = 1;
        for(int i = k; i>= 1; i--)
            sum *= i;
        int cnk = 1;
        for(int i = n; i>= n-k+1; i--)
        {
            cnk *= i;
        }
        for(int i = k ; i>= 1; i--)
        {
            cnk /= i;
        }
        sum = sum*cnk*cnk;
          cout<<sum<<endl;
    }
  }
   return 0;
}