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<cstring>
#include<algorithm>
using namespace std;
int n,k,mod,C[310][310],dp[310][310],sum[310];
int main()
{
	scanf("%d %d %d",&n,&k,&mod);
	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])>=mod?C[i][j]-=mod:0;
	}
	for(int i=k;~i;--i)
	{
		dp[i][1]=1;
		for(int j=1;j<=n+1;++j)
			for(int l=1;l<j;++l)
				dp[i][j]=(dp[i][j]+1ll*dp[i][j-l]*sum[l]%mod*C[j-2][l-1])%mod;
		for(int j=1;j<=n+1;++j)(sum[j]+=dp[i][j])>=mod?sum[j]-=mod:0;
	//	for(int j=1;j<=n+1;++j)printf("%d ",dp[i][j]);printf("\n");
	}
	printf("%d",dp[0][n+1]);
	return 0;
}
