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;
typedef long long LL;
const int N=305;
int f[N][N],c[N][N],s[N][N],n,m,MOD;

int main()
{
	scanf("%d%d%d",&n,&m,&MOD);
	for (int i=0;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[1][i]=1,s[1][i]=(m-i+1)%MOD;
	for (int i=2;i<=n+1;i++)
	{
		for (int j=0;j<=m;j++)
			for (int k=1;k<i;k++)
				f[i][j]=((LL)f[k][j]*s[i-k][j+1]%MOD*c[i-2][k-1]%MOD+f[i][j])%MOD;
		for (int j=m;j>=0;j--)
			s[i][j]=(s[i][j+1]+f[i][j])%MOD;
	}
	printf("%d\n",f[n+1][0]);
	return 0;
}
