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<iostream>
using namespace std;
#define N 310
typedef long long ll;
ll n, m, k;
class G {
public:
	ll g[N][N];
	void init() {
		for (int i = 0; i < N; i++)for (int j = 0; j < N; j++) {
			if (i == 0) { g[i][j] = 0; continue; }
			if (j == 0) { g[i][j] = 1; continue; }
			g[i][j] = g[i - 1][j] + g[i][j - 1]*i;
			g[i][j] %= m;
		}
	}
	ll qry(ll n, ll x) {
		return g[n][x];
	}
}; G g;
ll f[N][N];
int main() {
	cin >> n >> k >> m;
	g.init();
	for (int i = 0; i < N; i++)for (int j = 0; j < N; j++)f[i][j] = 0; f[0][0] = 1;
	for (int i = 0; i < N - 1; i++)for (int j = 0; j < N; j++) {
		for (int r = 0; r + j < N; r++) {
			f[i + 1][r + j] = (f[i + 1][r + j] + f[i][j] * g.qry(j+1, r))%m;
		}
	}
	cout << f[k][n] << endl;
	return 0;
}