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<algorithm>
#include<cstring>
#include<cmath>
#include<queue>
using namespace std;
#define N 1000002
typedef long long ll;
int n,k,p;
int dp[302][302],C[302][302],s[302][302];
int main()
{
	scanf("%d%d%d",&n,&k,&p);
	for(int i=0;i<=300;i++)C[i][0]=1;
	for(int i=1;i<=300;i++)for(int j=1;j<=i;j++)C[i][j]=(C[i-1][j]+C[i-1][j-1])%p;
	for(int i=0;i<=k;i++)dp[1][i]=1;
	for(int i=k;~i;i--)s[1][i]=(s[1][i+1]+dp[1][i])%p;
	for(int i=2;i<=n+1;i++)
	{
		for(int j=0;j<=k;j++)for(int ii=1;ii<i;ii++)
		dp[i][j]=(dp[i][j]+1ll*s[ii][j+1]*dp[i-ii][j]%p*C[i-2][ii-1]%p)%p;
		for(int j=k;~j;j--)s[i][j]=(s[i][j+1]+dp[i][j])%p;
	}
	printf("%d\n",dp[n+1][0]);
}
