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>
using namespace std;
#define ll long long

int n, k, mod, C[333][333], f[333][333], g[333][333];

template<class T1,class T2> void U(T1 &x,T2 y){
	x=(x+y)%mod;
}

int main(){
	cin>>n>>k>>mod;
	for (int i=0;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<=k;++i){
		f[1][i]=1;
		g[1][i]=i+1;
	}
	for (int i=2;i<=n+1;++i){
		for (int j=0;j<=k;++j){
			for (int i1=1;i1<i;++i1){
				int i2=i-i1;
				if (j) U(f[i][j],(ll)C[i-2][i1-1]*f[i1][j]%mod*g[i2][j-1]);
			}
			g[i][j]=f[i][j];
			if (j) U(g[i][j],g[i][j-1]);
		}
	}
	cout<<f[n+1][k]<<endl;
}