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:

• 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

Input:
1
4 1
Output:
3