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Let A = [a₁,a₂,...,a_n] 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 a_i>a_j. 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.

Task

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

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