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<cstdio>
#include<algorithm>
#include<cstring>
using namespace std;
int f[305][305],s[305][305],c[305][305];
int main(){
	int n,k,m;
	scanf("%d%d%d",&n,&k,&m);
	for(int i=0;i<=n;i++)
		for(int j=0;j<=i;j++)
			c[i][j]=(!j||j==i?1:c[i-1][j-1]+c[i-1][j])%m;
	for(int i=0;i<=k;i++)f[1][i]=1,s[1][i]=k-i+1;
	for(int i=2;i<=n+1;i++)
		for(int j=k;j>=0;j--){
			for(int l=1;l<i;l++)
				f[i][j]=(f[i][j]+1ll*s[l][j+1]*f[i-l][j]%m*c[i-2][l-1])%m;
			s[i][j]=(f[i][j]+s[i][j+1])%m;
		}
	printf("%d\n",f[n+1][0]);
}