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<cmath>
#include<cstring>
#include<algorithm>
#define ll long long
using namespace std;
int read()
{
	char ch=getchar();int f=0,x=1;
	while(ch<'0'||ch>'9'){if(ch=='-') x=-1;ch=getchar();}
	while(ch>='0'&&ch<='9'){f=(f<<1)+(f<<3)+ch-'0';ch=getchar();}
	return f*x;
}
int c[305][305],f[305][305],g[305][305],mod,n,k;

int main()
{
	n=read();k=read();mod=read();
	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]+c[i-1][j-1])%mod;
		}
	}
	for(int i=0;i<=k;i++)
	f[1][i]=1,g[1][i]=k-i+1;
	for(int i=2;i<=n+1;i++)
	{
		for(int j=k;j>=0;j--)
		{
			for(int l=1;l<i;l++)
			{
				f[i][j]+=1LL*f[i-l][j]*g[l][j+1]%mod*c[i-2][l-1]%mod;
				f[i][j]%=mod;
			}
			g[i][j]=(g[i][j+1]+f[i][j])%mod;
		}
	}
	cout<<f[n+1][0];
}
