Just Some Permutations 3

Given two integers N and M, find how many permutations of 1, 2, ..., N (first N natural numbers) are there where the sum of every two adjacent numbers is at most M. Input First line of the input contains an integer T which is the number of test cases. Each of the following T lines contain two integers N and M. Output For each test case output a single one line containing number of such permuta