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, k, M;
const int N = 500;
int C[N][N], F[N][N];
int main()
{
    cin >> n >> k >> M;
    for (int i = 0; i <= n; ++ i)
    {
        C[i][0] = C[i][i] = 1;
        for (int j = 1; j < i; ++ j)
            C[i][j] = (C[i - 1][j - 1] + C[i - 1][j]) % M;
    }
    for (int i = 0; i <= k; ++ i)
        F[0][i] = 1;
    for (int i = 1; i <= n; ++ i)
        for (int j = 0; j < i; ++ j)
            for (int p = 1, s = F[j][0]; p <= k; ++ p)
            {
                F[i][p] = (F[i][p] + 1ll * s * F[i - j - 1][p] % M * C[i - 1][j]) % M;
                s = (s + F[j][p]) % M;
            }
    cout << F[n][k] << endl;
}
