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, mod;
int dp[310][310], s[310][310];
int C[310][310];
int main() {
    scanf("%d%d%d", &n, &k, &mod);
    for (int i = 0; i <= n; i++) {
        C[i][i] = C[i][0] = 1;
        for (int j = 1; j < i; j++) C[i][j] = (C[i - 1][j] + C[i - 1][j - 1]) % mod;
    }
    for (int i = 0; i <= k; i++) dp[1][i] = 1;
    for (int i = 2; i <= n + 1; i++) {
        for (int j = k; j >= 0; j--) s[i - 1][j] = (dp[i - 1][j] + s[i - 1][j + 1]) % mod;
        for (int j = 0; j <= k; j++) {
            for (int f = 1; f < i; f++) dp[i][j] = (dp[i][j] + 1ll * dp[i - f][j] * s[f][j + 1] % mod * C[i - 2][f - 1]) % mod;
        }
    }
    return cout << dp[n + 1][0] << endl, 0;
}