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;

typedef long long ll;
const int MAXN = 310;

int n, k, m, c[MAXN][MAXN];
int f[MAXN][MAXN], sum[MAXN][MAXN];

int main()
{
	scanf("%d %d %d", &n, &k, &m);
	c[0][0] = 1;
	for(int i = 1; i < MAXN; ++i)
	{
		c[i][0] = c[i][i] = 1;
		for(int j = 1; j < i; ++j) c[i][j] = (c[i - 1][j] + c[i - 1][j - 1]) % m;
	}
	for(int i = k; ~i; --i)
	{
		f[i][0] = 1;
		for(int j = 1; j <= n; ++j)
			for(int t = 0; t < j; ++t)
				f[i][j] = (f[i][j] + (ll)sum[i + 1][j - t - 1] * f[i][t] % m * c[j - 1][t]) % m;
		for(int j = 0; j <= n; ++j)
			sum[i][j] = (sum[i + 1][j] + f[i][j]) % m;
	}
	printf("%d\n", f[0][n]);
	return 0;
}