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++