Welcome to ZOJ
Information
Select Problem
Runs
Ranklist
ZOJ Problem Set - 2284
Inversion Number

Time Limit: 2 Seconds      Memory Limit: 65536 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



Author: GUAN, Yao
Source: ZOJ Monthly, January 2005
Submit    Status