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;

int64_t MOD;
void add(int64_t& a, int64_t b){
    a = (a+b) % MOD;
}
void mul(int64_t& a, int64_t b){
    a = a*b % MOD;
}

int main(){
    int N, K;
    cin >> N >> K >> MOD;

    int64_t pow[302][302] = {0};
    for(int i=1; i<=301; i++){
        pow[i][0] = 1;
        for(int j=1; j<=301; j++) pow[i][j] = pow[i][j-1] * i % MOD;
    }

    int64_t sub[302][302] = {0};
    sub[0][0] = 1;
    for(int i=1; i<=301; i++) for(int j=0; j<=301; j++) for(int k=0; j+k<=301; k++) add(sub[i][j+k], sub[i-1][j] * pow[i][k]);

    int64_t dp[301][301] = {0};
    dp[0][0] = 1;
    for(int i=1; i<=300; i++) for(int j=0; j<=300; j++) for(int k=0; j+k<=300; k++) add(dp[i][j+k], dp[i-1][j] * sub[j+1][k]);

    cout << dp[K][N] << endl;
    return 0;
}
