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<iostream>
using namespace std;
int n, k, mod, i, j, ii;
int d[305][305], s[305][305], c[305][305];
int main(){
    cin>> n >> k >> mod;
    c[0][0] = 1;
    for(i = 1; i <= n; i++){
        c[i][0] = 1;
        for(j = 1; j <= i; j++){
            c[i][j] = (c[i - 1][j] + c[i - 1][j - 1]) % mod;
        }
    }
    for(i = k; i >= 0; i--){
        d[1][i] = 1;
        s[1][i] = s[1][i + 1] + 1;
    }
    for(i = 2; i <= n + 1; i++){
        for(j = k; j >= 0; j--){
            for(ii = 1; ii < i; ii++){
                d[i][j] = (d[i][j] + d[i - ii][j] * 1LL * s[ii][j + 1] % mod * c[i - 2][ii - 1]) % mod;
            }
            s[i][j] = (s[i][j + 1] + d[i][j]) % mod;
        }
    }
    cout<< d[n + 1][0];
}
