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>
#define ll long long
#define N 310
using namespace std;
ll C[N][N],mod;
ll f[N][N],g[N][N];
ll ksm(ll a,ll b=mod-2)
{
	ll ans=1;
	for(;b;b>>=1)
	{
		if(b&1) ans=ans*a%mod;
		a=a*a%mod;
	}
	return ans;
}
int main()
{
	int n,m;
	scanf("%d%d%lld",&n,&m,&mod);
	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;
	}
	for(int i=0;i<=m;i++)
	{
		f[1][i]=1;
		g[1][i]=m-i+1;
	}
	for(int i=2;i<=n+1;i++)
	{
		for(int j=0;j<=m;j++)
			for(int k=1;k<i;k++)
				f[i][j]=(f[i][j]+f[i-k][j]*g[k][j+1]%mod*C[i-2][k-1])%mod;
		for(int j=m;j>=0;j--)
			g[i][j]=(f[i][j]+g[i][j+1])%mod;
    }
    printf("%lld",f[n+1][0]);
	return 0;
}
