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 = 303;
int n, k, Mod, C[N][N], dp[N][N];
int main()
{
    scanf("%d%d%d", &n, &k, &Mod); n ++;
    for (int i = 0; i <= n; i ++)
        for (int j = C[i][0] = C[i][i] = 1; j < i; j ++)
            C[i][j] = (C[i - 1][j - 1] + C[i - 1][j]) % Mod;
    for (int i = 0; i <= n; i ++)
        dp[1][i] = 1;
    for (int l = 2; l <= k; l ++)
        for (int i = dp[l][0] = 1; i <= n; i ++)
            for (int j = 1; j <= i; j ++)
                dp[l][i] = (dp[l][i] + 1LL * C[i - 1][j - 1] * dp[l - 1][j] % Mod * dp[l][i - j]) % Mod;
    return !printf("%d\n", dp[k][n]);
}