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>
using namespace std;
int n, m, mod;
void Add(int &x, int y) { (x += y) >= mod ? x -= mod : x; }
int f[302][302][302];
int main() {
    scanf("%d%d%d", &n, &m, &mod);
    f[0][1][0] = 1;
    for (int i = 0; i <= n; ++i)
        for (int j = 1; j <= m; ++j)
            for (int k = i; k >= 0; --k)
                k ? Add(f[i][j][k - 1], f[i][j][k])
                  : Add(f[i][j + 1][i], f[i][j][k]),
                    Add(f[i + 1][j][k], 1ll * f[i][j][k] * (k + 1) % mod);
    printf("%d", f[n][m][0]);
    return 0;
}