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 <cassert>
#include <cstring>
#include <algorithm>
#define meow(args...) fprintf(stderr, args)
unsigned c[305][305], f[305][305], g[305][305];
int main()
{
	int n, k;
	unsigned m;
	register int i, j, l;
	scanf("%d%d%u", &n, &k, &m);
	for(i=0; i<=k; ++i) f[0][i]=1;
	for(i=0; i<=k; ++i) g[0][i]=i+1;
	for(i=0; i<=n; ++i) {
		c[i][0]=c[i][i]=1;
		for(j=1; j<i; ++j) c[i][j]=(c[i-1][j-1]+c[i-1][j])%m;
	}
	for(i=1; i<=n; ++i) {
		for(j=1; j<=k; ++j) {
			f[i][j]=0;
			for(l=0; l<i; ++l) f[i][j]=(f[i][j]+(unsigned long long)f[l][j]*g[i-l-1][j-1]%m*c[i-1][l])%m;
			g[i][j]=(f[i][j]+g[i][j-1])%m;
		}
	}
	printf("%d\n", f[n][k]);
	return 0;
}
