Codeforces celebrates 10 years! We are pleased to announce the crowdfunding-campaign. Congratulate us by the link https://codeforces.com/10years.
×

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

H. Ember and Storm's Tree Game

time limit per test

3 secondsmemory limit per test

512 megabytesinput

standard inputoutput

standard outputEmber and Storm play a game. First, Ember picks a labelled tree *T* of *n* vertices, such that the degree of every vertex is at most *d*. Then, Storm picks two distinct vertices *u* and *v* in this tree and writes down the labels of the vertices in the path from *u* to *v* in a sequence *a*_{1}, *a*_{2}... *a*_{k}. Finally, Ember picks any index *i* (1 ≤ *i* < *k*) in the array. Now he performs one of the following two operations exactly once:

- flip the subrange [
*i*+ 1,*k*] and add*a*_{i}to it. After this, the sequence becomes*a*_{1}, ...*a*_{i},*a*_{k}+*a*_{i},*a*_{k - 1}+*a*_{i}, ...*a*_{i + 1}+*a*_{i} - negate the subrange [
*i*+ 1,*k*] and add*a*_{i}to it. i.e., the array becomes*a*_{1}, ...*a*_{i}, -*a*_{i + 1}+*a*_{i}, -*a*_{i + 2}+*a*_{i}, ... -*a*_{k}+*a*_{i}

Ember wins if the array is monotonically increasing or decreasing after this. Otherwise Storm wins.

The game can be described by the tuple (*T*, *u*, *v*, *i*, *op*) where *op* is «flip» or «negate» depending on the action Ember chose in the last turn. Find the number of tuples that can occur if Ember and Storm play optimally. When they play optimally, if there are multiple moves by which they are guaranteed to win, then they may play any of the winning moves. Otherwise, if someone loses no matter what they play, then they may play any of the possible moves.

Report the answer modulo *m*.

Input

The input consists of a single line containing three integers *n*, *d* and *m* (2 ≤ *n* ≤ 200, 1 ≤ *d* < *n*, 1 ≤ *m* ≤ 2·10^{9}).

Output

Print a single number — the number of possible tuples if Ember and Storm play as described, modulo *m*.

Examples

Input

2 1 1000000007

Output

4

Input

3 1 250

Output

0

Input

3 2 100

Output

36

Note

In the first sample case, there is only one possible tree. There are two possible paths, 1 to 2 and 2 to 1. For both paths, *i* can only be 1, and *op* can take both possibilities. Therefore, the answer is 4.

In the second sample, there are no possible trees.

In the third sample, there are three possible trees.

Codeforces (c) Copyright 2010-2020 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Feb/25/2020 23:00:12 (e2).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|