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 <cstring>
#include <cstdio>
#define ll long long
using namespace std;

inline int read(){
	int sum=0,f=1;char c=getchar();
	while(c>'9'||c<'0'){if(c=='-') f=-1;c=getchar();}
	while(c<='9'&&c>='0'){sum=sum*10+c-'0';c=getchar();}
	return f*sum;
}

const int N=305;
int n,m,K;
int f[N][N][N];

signed main(){
	n=read();K=read();m=read();
	f[0][1][0]=1;
	for(int i=0;i<=n;i++){
		for(int j=1;j<=K;j++){
			for(int k=i;k>=0;k--){
				if(k) f[i][j][k-1]=(f[i][j][k-1]+f[i][j][k])%m;
				else f[i][j+1][i]=(f[i][j+1][i]+f[i][j][k])%m;
				f[i+1][j][k]=(f[i+1][j][k]+1ll*f[i][j][k]*(k+1)%m)%m;
			}
		}
	}
	printf("%d\n",f[n][K][0]);
	return 0;
}
