Petr’s problem

A permutation $p_1, \dots, p_n$ is a sequence of numbers between 1 and $n$ such that each number appears exactly once. An inversion in a permutation is a pair of indices $(i, j)$ such that $i < j$ but $p_i > p_j$ . The weight of an inversion $(i, j)$ is $j - i$ .

How many permutations of $n$ elements exist where the sum of weights of all inversions is equal to $x$ ? For instance, there are exactly two such permutations for $n = 4$ and $x = 4$ : 3, 2, 1, 4 and 1, 4, 3, 2.

Input

Input consists of several cases, each one with $n$ and $x$ . You can assume $1 \le n \le 14$ and $0 \le x \le (n + 1)n(n - 1)/6$ .

Output

For every case, print the number of permutations of $n$ elements such that the sum of weights of all inversions is $x$ .

Problem information

Author: Petr Mitrichev

Generation: 2026-01-25T12:00:00.215Z