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 MN = 302;

int N, K, M;
int comb[MN][MN], fact[MN];

int cc[MN][MN];
int dp(int val, int cnt) {
    if(val == K + 1) return cnt == 0;
    int &ret = cc[val][cnt];
    if(ret != -1) return ret;

    ret = dp(val + 1, cnt);
    for(int i = 0; i < cnt; i++) {
        ret += 1LL * comb[cnt][i] * dp(val + 1, i) % M * dp(val, cnt - 1 - i) % M;
        ret %= M;
    }
    return ret;
}

int main() {
    cin >> N >> K >> M;

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

    memset(cc, -1, sizeof(cc));
    printf("%d", dp(1, N));
}
