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<cstdlib>
#include<cstring>
#include<algorithm>
using namespace std;
int mod;
int dp[303][303];
int sum[303][303];
int c[303][303];
int main()
{
	int n,k;
	scanf("%d%d%d",&n,&k,&mod);
	memset(c,0,sizeof(c));
	c[0][0]=1;
	for(int i=1;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;
	}
	memset(dp,0,sizeof(dp));
	for(int i=0;i<=k;i++)
		dp[0][i]=1;
	memset(sum,0,sizeof(sum));
	for(int i=k;i>=0;i--)
		sum[0][i]=(sum[0][i+1]+dp[0][i])%mod;
	for(int i=1;i<=n;i++)
	{
		for(int j=0;j<=k;j++)
			for(int kk=1;kk<=i;kk++)
				dp[i][j]=((long long)sum[kk-1][j+1]*dp[i-kk][j]%mod*c[i-1][kk-1]+dp[i][j])%mod;
		for(int j=k;j>=0;j--)
			sum[i][j]=(sum[i][j+1]+dp[i][j])%mod;
	}
	printf("%d",dp[n][0]);
	return 0;
}