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<cstdio>
#include<algorithm>
#include<cstring>
#define ll long long
using namespace std;
int n,k;
ll MOD,f[305][305],c[305][305],sum[305][305];
int main()
{
	scanf("%d%d%lld",&n,&k,&MOD);
	c[0][0]=1;
	for(int i=0;i<=300;i++)
	for(int j=0;j<=300;j++)
	{
		if(c[i][j]>=MOD)c[i][j]-=MOD;
		c[i+1][j+1]+=c[i][j];
		c[i+1][j]+=c[i][j];
	}
	for(int i=k;i>=0;i--)
	{
		f[1][i]=1;
		sum[1][i]=sum[1][i+1]+1;
	}
	for(int i=2;i<=n+1;i++)
	{
		for(int j=k-1;j>=0;j--)
		{
			for(int s=1;s<i;s++)
			  f[i][j]=(f[i][j]+f[i-s][j]*sum[s][j+1]%MOD*c[i-2][s-1])%MOD;
			sum[i][j]=(sum[i][j+1]+f[i][j])%MOD;
		}
	}
	printf("%lld\n",f[n+1][0]);
	return 0;
}