## PERMUT1 - Permutations

Let A = [a1,a2,...,an] be a permutation of integers 1,2,...,n. A pair of indices (i,j), 1<=i<=j<=n, is an inversion of the permutation A if ai>aj. We are given integers n>0 and k>=0. What is the number of n-element permutations containing exactly k inversions?

For instance, the number of 4-element permutations with exactly 1 inversion equals 3.

Write a program which for each data set from a sequence of several data sets:

• reads integers n and k from input,
• computes the number of n-element permutations with exactly k inversions,
• writes the result to output.

### Input

The first line of the input file contains one integer d, 1<=d<=10, which is the number of data sets. The data sets follow. Each data set occupies one line of the input file and contains two integers n (1<=n<=12) and k (0<=k<=98) separated by a single space.

### Output

The i-th line of the output file should contain one integer - the number of n-element permutations with exactly k inversions.

### Example

```Sample input:
1
4 1

Sample output:
3
```