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<iostream>
#include<algorithm>
#include<cstdio>
#include<cstring>
using namespace std;
int Mod;
int n,m;
int C[310][310];
int f[310][310],F[310][310];
int main()
{
	cin>>n>>m>>Mod;
	C[0][0]=1;
	for(int i=1;i<=n;i++)
	{
		C[i][0]=1;
		for(int j=1;j<=i;j++)
			C[i][j]=(C[i-1][j-1]+C[i-1][j])%Mod;
	}
	for(int i=0;i<=m;i++)
		f[0][i]=1;
	for(int i=1;i<=n;i++)
	{
		F[i-1][0]=f[i-1][0];
		for(int j=1;j<=m;j++)
			F[i-1][j]=(F[i-1][j-1]+f[i-1][j])%Mod;
		for(int j=1;j<=m;j++)
			for(int k=1;k<=i;k++)
				f[i][j]=(f[i][j]+(long long)C[i-1][k-1]*F[k-1][j-1]%Mod*f[i-k][j])%Mod;
	}
	printf("%d\n",f[n][m]);
	return 0;
}