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>
const int maxn = 1010;
typedef long long ll;
int n, k, mod;
int g[maxn], f[maxn];
int C[maxn][maxn];
inline void reduce(int & x){ x += x >> 31 & mod; }
inline void exp(int * g) {
	memcpy(f, g, sizeof f);
	for(int i = 0;i <= n + 1;++i) {
		for(int j = 0;j < i;++j) {
			g[i] = (g[i] + (ll) f[j] * g[i - j - 1] % mod * C[i][j]) % mod;
		}
	}
}
int main() {
	std::cin >> n >> k >> mod;
	for(int i = 0;i < maxn;++i) for(int j = C[i][0] = 1;j <= i;++j)
		reduce(C[i][j] = C[i - 1][j] + C[i - 1][j - 1] - mod);
	std::fill(g, g + n + 2, 1);
	for(int i = 1;i < k;++i) exp(g);
	std::cout << g[n] << '\n';
}
