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;
int n,k,M,i,j,m;
long long dp[305][305],f[305][305];
int main()
{
	scanf("%d %d %d",&n,&k,&M);
	for(i=0;i<=n;++i)
		f[0][i]=1;
	for(i=1;i<=n;++i)
		for(j=0;j<=n;++j)
		{
			long long s=1;
			for(m=0;m<=j;++m)
			{
				f[i][j]=(f[i][j]+f[i-1][j-m]*s)%M;
				s=s*(i+1)%M;
			}
		}
	dp[0][0]=1;
	for(i=1;i<=k;++i)
		for(j=0;j<=n;++j)
			for(m=0;m<=j;++m)
				dp[i][j]=(dp[i][j]+dp[i-1][j-m]*f[j-m][m])%M;
	cout<<dp[k][n]<<endl;
}
