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;
long long dp[307][307],c[307][307],s[307][307];
int main(){
	long long n,k,m,i,j,p;
	cin>>n>>k>>m;
	c[0][0]=1;
	for (i=1;i<=300;i++){
		c[i][0]=1;
		for (j=1;j<=i;j++){
			(c[i][j]=c[i-1][j]+c[i-1][j-1])%=m;
		}
	}
	for (i=k;i>-1;i--){
		dp[1][i]=1;
		s[1][i]=s[1][i+1]+1;
	}
	for (i=2;i<=n+1;i++){
		for (j=0;j<=k;j++){
			for (p=1;p<i;p++){
				(dp[i][j]+=dp[i-p][j]*c[i-2][p-1]%m*s[p][j+1])%=m;
			}
		}
		for (j=k;j;j--){
			(s[i][j]=s[i][j+1]+dp[i][j])%=m;
		}
	}
	cout<<dp[n+1][0]<<endl;
	return 0;
}