# Permutations with given distance

Butt-head has n volumes of his favourite Encyclopedia For Stupid Teenagers. The volumes are numbered from 1 to n and arranged in a row. He doesn’t like strict order, but he dislikes complete chaos as well. Butt-head counts the distance of volumes’ pertmutation as the sum of differences between number and position for all volumes. In other words, if the permutation is (i_1, i_2, ... i_n), where i_k (1 ≤ k ≤ n) denotes the number of volume on k-th place, then its distance will be |i_1–1|+|i_2–2|+...+|i_n–n|. Butt-head has a favourite number d, and he wants to arrange the Encyclopedia volumes so, that the distance will be equal to d. In how many ways can he do this?

## Input

First line of input contains the quantity of tests T (1 ≤ T ≤ 100). Each of the next T lines contains data for one test: the quantity of volumes n (1 ≤ n ≤ 50) and the required distance d (0 ≤ d ≤ 10000), separated by a space. Numbers n, d are integer.

## Output

Output T lines of the form "Case #A: B", where A is the number of test (beginning from 1), B is the quantity of permutations of n volumes with distance d, taken modulo 100007.