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<stdio.h>
int f[512],g[512];
int c[305][305];
int main()
{
	int n,k,m;
	scanf("%d%d%d",&n,&k,&m);
	n++;
	k++;
	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];
			if(c[i][j]>=m)
			{
				c[i][j]-=m;
			}
		}
	}
	while(k--)
	{
		f[1]=1;
		for(int i=2;i<=n;i++)
		{
			f[i]=0;
			for(int j=1;j<i;j++)
			{
				int inc=(long long)g[j]*f[i-j]%m;
				f[i]+=(long long)inc*c[i-2][j-1]%m;
				if(f[i]>=m)
				{
					f[i]-=m;
				}
			}
		}
		for(int i=1;i<=n;i++)
		{
			g[i]+=f[i];
			if(g[i]>=m)
			{
				g[i]-=m;
			}
		}
	}
	printf("%d\n",f[n]);
	return 0;
}