Permutation Inversions

Your task is to count the number of permutations of 1,2,\dots,n that have exactly k inversions (i.e., pairs of elements in the wrong order). For example, when n=4 and k=3, there are 6 such permutations: - [1,4,3,2] - [2,3,4,1] - [2,4,1,3] - [3,1,4,2] - [3,2,1,4] - [4,1,2,3] Input The only input line has two integers n and k. Output Print the answer modulo 10^9+7. Constraints - 1 \le n