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 FOR(i,a,b) for(ll i=(a);i<(b);i++)
#define REP(i,a) FOR(i,0,a)

using namespace std;

typedef long long ll;

const ll MAX_N=300,MAX_K=300;

ll N,K,M;

ll dp[MAX_N+1][MAX_K+1][MAX_N+1];

int main(){
	cin>>N>>K>>M;
	memset(dp,0,sizeof(dp));
	FOR(k,1,K+1){		
		FOR(n,1,N+1){
			for(ll m=n;m>0;m--){
				ll x;
				if (n==1){
					x=k%M;
				}else if (n==m){
					if (k==1){
						x=0;
					}else{
						x=(dp[n-1][k-1][1]*n+dp[n][k-1][1])%M;
					}
				}else{
					x=(dp[n-1][k][m]*m+dp[n][k][m+1])%M;
				}
				dp[n][k][m]=x;
			}
		}
	}
	cout<<dp[N][K][1]<<endl;
	return 0;
}