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>
#define LL long long
using namespace std;
const int maxn = 3e2 + 5;
 
int mod, n, k;
LL dp[maxn][maxn][maxn], ans;
 
int main() {
	scanf("%d%d%d", &n, &k, &mod);
	dp[0][1][0] = 1;
	for(register int i = 0; i <= n; ++i)
		for(register int j = 1; j <= k; ++j)
			for(register int p = i; p >= 0; --p) {
				if(p) (dp[i][j][p - 1] += dp[i][j][p]) %= mod;
				else (dp[i][j + 1][i] += dp[i][j][p]) %= mod;
				(dp[i + 1][j][p] += dp[i][j][p] * (p + 1)) %= mod;
			}
	printf("%lld", dp[n][k + 1][n]);
	return 0;
}
