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<cstdio>
#include<algorithm>
#include<cmath>
#include<cstring>
#define ll long long
using namespace std;
const int N=310;
int n,K,mo,C[N][N],f[N][N],sum[N][N];
int main()
{
	scanf("%d%d%d",&n,&K,&mo);
	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]+C[i-1][j-1])%mo;
	}
	for (int i=0;i<=K;i++) f[1][i]=1,sum[1][i]=i+1;
	for (int i=2;i<=n+1;i++)
		for (int j=0;j<=K;j++)
		{
			for (int k=1;k<=i-1;k++)
				f[i][j]=(f[i][j]+(ll)f[i-k][j]*C[i-2][k-1]%mo*(sum[k][K]-sum[k][j])%mo)%mo;
			sum[i][j]=(sum[i][j-1]+f[i][j])%mo;
		}
	printf("%d\n",(f[n+1][0]+mo)%mo);
	return 0;
}
