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[310][310],dpc[310][310];
long long ncr[310][310];
int N,K,M;

int main(){
	cin>>N>>K>>M;
	ncr[1][0] = ncr[1][1] = ncr[0][0] = 1;
	for(int i=2;i<310;i++){
		ncr[i][0] = 1;
		for(int j=1;j<=i;j++) ncr[i][j] = (ncr[i-1][j] + ncr[i-1][j-1])%M;
	}

	for(int i=0;i<=K;i++) dp[1][i] = 1;
	for(int i=K;i>=0;i--) dpc[1][i] = dp[1][i] + dpc[1][i+1];
	for(int i=2;i<=N+1;i++) for(int j=K;j>=0;j--){
		for(int k=1;k<i;k++) dp[i][j] += (dp[i-k][j]*dpc[k][j+1]%M)*ncr[i-2][k-1]%M;
		dp[i][j] %= M;
		dpc[i][j] = (dp[i][j] + dpc[i][j+1])%M;
	}
	
	cout<<dp[N+1][0]<<endl;
	return 0;
}