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>

typedef long long ll;
const int N=310;

int C[N][N],fact[N];
int f[N],g[N];

int n,k,MOD;

inline void inc(int a,int &b){b=(a+b)%MOD;}

int main()
{
	scanf("%d%d%d",&n,&k,&MOD);

	for(int i=0;i<N;i++)C[i][0]=1;
	for(int i=1;i<N;i++)
		for(int j=1;j<N;j++)
			C[i][j]=(C[i-1][j-1]+C[i-1][j])%MOD;
	fact[0]=1;
	for(int i=1;i<N;i++)fact[i]=(ll)fact[i-1]*i%MOD;

	g[1]=1;

	for(int val=k-1;~val;val--)
	{
		memset(f,0,sizeof(f));
		f[0]=1;

		for(int i=1;i<=n;i++)
			for(int j=1;j<=i;j++)
				inc((ll)g[j]*f[i-j]%MOD*C[i-1][j-1]%MOD,f[i]);

		for(int i=n+1;i;i--)f[i]=f[i-1],f[i-1]=0;
		for(int i=1;i<=n+1;i++)
			inc(f[i],g[i]);

//		for(int i=1;i<=n+1;i++)
//			printf("%d ",f[i]);
//		printf("\n");
	}

	printf("%d\n",f[n+1]);

	return 0;
}
