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;

const int maxn = 310;
int n, K, P, f[maxn][maxn], s[maxn][maxn], C[maxn][maxn];

int main() {
    scanf("%d %d %d", &n, &K, &P);
    for (int i = 0; i <= n; i++) {
        for (int j = C[i][0] = 1; j <= i; j++) {
            C[i][j] = (C[i - 1][j - 1] + C[i - 1][j]) % P;
        }
    }
    for (int i = 0; i <= K; i++) {
        f[1][i] = 1, s[1][i] = K - i + 1;
    }
    for (int i = 2; i <= n + 1; i++) {
        for (int j = 1; j < i; j++) {
            for (int k = 0; k <= K; k++) {
                f[i][k] = (f[i][k] + 1LL * f[i - j][k] * s[j][k + 1] % P * C[i - 2][j - 1]) % P;
            }
        }
        for (int j = K; j; j--) s[i][j] = (s[i][j + 1] + f[i][j]) % P;
    }
    printf("%d\n", f[n + 1][0]);
    return 0;
}