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 <cstdio>

#define MAXN 309

int comb[MAXN][MAXN], dp[MAXN][MAXN], s[MAXN][MAXN];

int main() {
    int n, k, mod;
    scanf("%d%d%d", &n, &k, &mod);

    for (int i = 0; i <= n; i++) {
        comb[i][0] = 1;
        for (int j = 1; j <= i; j++)
            comb[i][j] = (comb[i - 1][j - 1] + comb[i - 1][j]) % mod;
    }

    for (int i = 0; i <= k; i++)
        dp[0][i] = 1;
    for (int i = k; i >= 0; i--)
        s[0][i] = (s[0][i + 1] + dp[0][i]) % mod;

    for (int i = 1; i <= n; i++) {
        for (int j = 0; j <= k; j++)
            for (int p = 1; p <= i; p++)
                dp[i][j] = (dp[i][j] + 1LL * s[p - 1][j + 1] * comb[i - 1][p - 1] % mod * dp[i - p][j]) % mod;
        for (int j = k; j >= 0; j--)
            s[i][j] = (dp[i][j] + s[i][j + 1]) % mod;
    }

    printf("%d\n", dp[n][0]);

    return 0;
}
