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<cstring>
using namespace std;
int n,k,mod;
int C[310][310],f[310][310],s[310][310];
int main()
{
	scanf("%d%d%d",&n,&k,&mod);
	C[0][0]=1;
	for (int i=1;i<=n;i++)
	{
		C[0][i]=1;
		for (int j=1;j<=i;j++)
			C[j][i]=(C[j-1][i-1]+C[j][i-1])%mod;
	}
	for (int i=0;i<=k;i++) f[1][i]=1,s[1][i]=i;
	for (int i=2;i<=n+1;i++)
		for (int j=0;j<=k;j++)
		{
			int ans=0;
			for (int siz=1;siz<=i-1;siz++)
				ans=(1ll*C[siz-1][i-2]*f[i-siz][j]%mod*(s[siz][k]-s[siz][j]+mod)%mod+ans)%mod;
			f[i][j]=ans;
			s[i][j]=ans;
			if (j) s[i][j]=(ans+s[i][j-1])%mod;
		}
	printf("%d",f[n+1][0]);
}
