Abnormal Permutation Pairs (easy version)

ID: 5984

Type: RemoteJudge

1000ms

512MiB

Tried: 0

Accepted: 0

Difficulty: (None)

Uploaded By:

Hydro

Tags>

combinatorics

fft

math

*2400

No submission language available for this problem.

Description

This is the easy version of the problem. The only difference between the easy version and the hard version is the constraints on $n$ . You can only make hacks if both versions are solved.

A permutation of $1, 2, \ldots, n$ is a sequence of $n$ integers, where each integer from $1$ to $n$ appears exactly once. For example, $[2,3,1,4]$ is a permutation of $1, 2, 3, 4$ , but $[1,4,2,2]$ isn't because $2$ appears twice in it.

Recall that the number of inversions in a permutation $a_1, a_2, \ldots, a_n$ is the number of pairs of indices $(i, j)$ such that $i < j$ and $a_i > a_j$ .

Let $p$ and $q$ be two permutations of $1, 2, \ldots, n$ . Find the number of permutation pairs $(p,q)$ that satisfy the following conditions:

$p$ is lexicographically smaller than $q$ .
the number of inversions in $p$ is greater than the number of inversions in $q$ .

Print the number of such pairs modulo $mod$ . Note that $mod$ may not be a prime.

The only line contains two integers $n$ and $mod$ ( $1\le n\le 50$ , $1\le mod\le 10^9$ ).

Print one integer, which is the answer modulo $mod$ .

Input

The only line contains two integers $n$ and $mod$ ( $1\le n\le 50$ , $1\le mod\le 10^9$ ).

Output

Print one integer, which is the answer modulo $mod$ .

Samples

Sample Input 1

4 403458273

Sample Output 1

Note

The following are all valid pairs $(p,q)$ when $n=4$ .

$p=[1,3,4,2]$ , $q=[2,1,3,4]$ ,
$p=[1,4,2,3]$ , $q=[2,1,3,4]$ ,
$p=[1,4,3,2]$ , $q=[2,1,3,4]$ ,
$p=[1,4,3,2]$ , $q=[2,1,4,3]$ ,
$p=[1,4,3,2]$ , $q=[2,3,1,4]$ ,
$p=[1,4,3,2]$ , $q=[3,1,2,4]$ ,
$p=[2,3,4,1]$ , $q=[3,1,2,4]$ ,
$p=[2,4,1,3]$ , $q=[3,1,2,4]$ ,
$p=[2,4,3,1]$ , $q=[3,1,2,4]$ ,
$p=[2,4,3,1]$ , $q=[3,1,4,2]$ ,
$p=[2,4,3,1]$ , $q=[3,2,1,4]$ ,
$p=[2,4,3,1]$ , $q=[4,1,2,3]$ ,
$p=[3,2,4,1]$ , $q=[4,1,2,3]$ ,
$p=[3,4,1,2]$ , $q=[4,1,2,3]$ ,
$p=[3,4,2,1]$ , $q=[4,1,2,3]$ ,
$p=[3,4,2,1]$ , $q=[4,1,3,2]$ ,
$p=[3,4,2,1]$ , $q=[4,2,1,3]$ .

#P1542E1. Abnormal Permutation Pairs (easy version)

Description

Input

Output

Samples

Note

Status

Development

Support

#P1542E1. Abnormal Permutation Pairs (easy version)

Abnormal Permutation Pairs (easy version)

Description

Input

Output

Samples

Sample Input 1

Sample Output 1

Note

Status

Development

Support

Don't have an account?

SIGN IN