4879번 - PERMS 다국어

문제

Count the number of permutations that have a specific number of inversions.

Given a permutation a₁, a₂, a₃,..., a_n of the n integers 1, 2, 3, ..., n, an inversion is a pair (a_i, a_j) where i < j and a_i > a_j. The number of inversions in a permutation gives an indication on how "unsorted" a permutation is. If we wish to analyze the average running time of a sorting algorithm, it is often useful to know how many permutations of n objects will have a certain number of inversions.

In this problem you are asked to compute the number of permutations of n values that have exactly k inversions.

For example, if n = 3, there are 6 permutations with the indicated inversions as follows:

Therefore, for the permutations of 3 things

• 1 of them has 0 inversions
• 2 of them have 1 inversion
• 2 of them have 2 inversions
• 1 of them has 3 inversions
• 0 of them have 4 inversions
• 0 of them have 5 inversions
• etc.

입력

The input consists one or more problems. The input for each problem is specified on a single line, giving the integer n (1 <= n <= 18) and a non-negative integer k (0 <= k <= 200). The end of input is specified by a line with n = k = 0.

출력

For each problem, output the number of permutations of {1, ..., n}with exactly k inversions.

제한

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