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 <bits/stdc++.h>
#define int long long
using namespace std;
const int N=400;
int n,k,mod,dp[N][N][N];
inline void add(int &a,int b){a=(a+b)%mod;}
inline void del(int &a,int b){a=(a-b+mod)%mod;}
inline void mul(int &a,int b){a=(a*b)%mod;}
signed main()
{
	scanf("%lld%lld%lld",&n,&k,&mod);
	dp[0][1][0]=1;
	for (int i=0;i<=n;i++)
	{
		for (int j=1;j<=k;j++)
		{
			for (int p=i;p>=0;p--)
			{
				if (p>0) add(dp[i][j][p-1],dp[i][j][p]);
				else add(dp[i][j+1][i],dp[i][j][p]);
				add(dp[i+1][j][p],dp[i][j][p]*(p+1)%mod);
			}
		}
	}
	printf("%lld\n",dp[n][k+1][n]);
}
