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>

typedef long long ll;
const int N = 354;

int mod;
int n, R;
int C[N][N];
int f[N], B1[N];

inline void add(int &x, const int y) {x += y - mod, x += x >> 31 & mod;}

void init(int n) {
	int i, j;
	for (*C[0] = i = 1; i <= n; ++i)
		for (*C[i] = j = 1; j <= n; ++j)
			add(C[i][j] = C[i - 1][j], C[i - 1][j - 1]);
}

void Exp(int *a) {
	int i, j; memcpy(B1, a, n << 2);
	for (i = 0; i <= n; ++i)
		for (j = 0; j < i; ++j)
			a[i] = (a[i] + (ll)B1[j] * a[i - j - 1] % mod * C[i][j]) % mod;
}

int main() {
	scanf("%d%d%d", &n, &R, &mod), init(++n);
	for (std::fill(f, f + n, 1); --R; Exp(f));
	return printf("%d\n", f[--n]), 0;
}