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 <cstring>
#include <cstdlib>
#include <algorithm>
#define LL long long
using namespace std;
const LL Maxn = 310;
LL f[Maxn][Maxn], s[Maxn][Maxn];
LL n, K, Mod;
LL C[Maxn][Maxn];
void up(LL &x, LL y) { x = (x + y) % Mod; }
int main() {
	LL i, j, k;
	scanf("%lld%lld%lld", &n, &K, &Mod);
	n++;
	C[0][0] = 1;
	for(i = 1; i <= n; i++){
		C[i][0] = 1;
		for(j = 1; j <= i; j++) C[i][j] = (C[i-1][j-1]+C[i-1][j])%Mod;
	}
	for(i = 0; i <= K; i++) f[1][i] = 1;
	for(i = K; i >= 0; i--) s[1][i] = (s[1][i+1]+f[1][i])%Mod;
	for(i = 2; i <= n; i++){
		for(j = 0; j <= K; j++){
			for(k = 1; k < i; k++) up(f[i][j], C[i-2][k-1]*f[i-k][j]%Mod*s[k][j+1]);
		}
		for(j = K; j >= 0; j--) s[i][j] = (s[i][j+1]+f[i][j])%Mod;
	}
	printf("%lld\n", f[n][0]);
	return 0;
}