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 N = 310;

typedef long long LL;

int dp[N][N], C[N][N], sum[N][N];

int main() {
    int n, k, mod; scanf("%d%d%d", &n, &k, &mod), n++;
    for (int i = 0; i <= n; 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++) sum[1][i] = k - i + 1, dp[1][i] = 1;
    for (int i = 2; i <= n; i++) {
        for (int j = 0; j <= k; j++) {
            for (int t = 1; t < i; t++) 
                dp[i][j] = (dp[i][j] + (LL)dp[i - t][j] * C[i - 2][t - 1] % mod * sum[t][j + 1]) % mod;
        }
        for (int j = k; j >= 1; j--) sum[i][j] = (sum[i][j + 1] + dp[i][j]) % mod;
    }
    printf("%d\n", dp[n][0]);
    return 0;
}
