Find the number of the possible tuples of sequences (A_0,A_1,...,A_N) that satisfy all of the following conditions, modulo M:

* For every i (0\leq i\leq N), A_i is a sequence of length i consisting of integers between 1 and K (inclusive);
* For every i (1\leq i\leq N), A_{i-1} is a subsequence of A_i, that is, there exists 1\leq x_i\leq i such that the removal of the x_i-th element of A_i would result in a sequence equal to A_{i-1};
* For every i (1\leq i\leq N), A_i is lexicographically larger than A_{i-1}.

Constraints

* 1 \leq N,K \leq 300
* 2 \leq M \leq 10^9
* N, K and M are integers.

Input

Input is given from Standard Input in the following format:


N K M


Output

Print the number of the possible tuples of sequences (A_0,A_1,...,A_N), modulo M.

Examples

Input

2 2 100


Output

5


Input

4 3 999999999


Output

358


Input

150 150 998244353


Output

186248260
#include<bits/stdc++.h>
using namespace std;

#define int long long

const int inf=1000000007ll;
int mod;

inline void add(int& x,int y)
{
	x+=y;
	if(x>mod) x-=mod;
}

int N,M;
int dp[333][333][333];

signed main()
{
	ios::sync_with_stdio(false);
	
	cin>>N>>M>>mod;
	dp[0][1][0]=1;
	for(int i=0;i<=N;i++)
	{
		for(int j=1;j<=M;j++)
		{
			for(int k=i;k>=0;k--)
			{
				int& cur=dp[i][j][k];
				if(!cur) continue;
				if(!k) add(dp[i][j+1][i],cur);
				else add(dp[i][j][k-1],cur);
				if(i+1<=N) add(dp[i+1][j][k],cur*(k+1)%mod);
			}
		}
	}
	cout<<dp[N][M][0]<<endl;
	return 0;
}










