Inversion Number

Time Limit: 1 Second    Memory Limit: 32768 KB

Let { A1,A2,...,An } be a permutation of the set{ 1,2,..., n}. The inversion number of the permutation is the number of integer pairs (i,j) that satisfy 1<=i<j<=n and Ai>Aj.

Your task is to calculate how many n-permutations has an inversion number of k.

Input

The input consists of several test cases. Each test case contains two integers n(0<n<=20) and k(0<=k<=200), which are mentioned above. Input is terminated by n=m=0, which should not be proceeded.

Output

For each case of input output the number of n-permutations that has an inversion number of k in one line.

Sample Input

2 0 
5 3 
0 0 

Sample Output

1 
15 

Submit

Source: ZOJ Monthly, January 2005