A permutation p_{1}, …, 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 ≤ n ≤ 14 and 0 ≤ x ≤ (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.

Public test cases

**Input**

4 4 1 0 14 455 14 200

**Output**

2 1 1 486253544

Information

- Author
- Petr Mitrichev
- Language
- English
- Official solutions
- C++
- User solutions
- C++