Problem:
Score : 1200 points

Problem Statement

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.

Sample Input 1

2 2 100

Sample Output 1

5

Five tuples below satisfy the conditions:

(),(1),(1,1)

(),(1),(1,2)

(),(1),(2,1)

(),(2),(2,1)

(),(2),(2,2)

Sample Input 2

4 3 999999999

Sample Output 2

358

Sample Input 3

150 150 998244353

Sample Output 3

186248260

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
using namespace std;

const int N = 305;

int n, K, mod;
int f[N][N], c[N][N], prf[N][N];

int main() {
	ios_base::sync_with_stdio(false);
	cin >> n >> K >> mod; n++, K++;
	for (int i = 0;i <= n;++i){
		c[i][0] = 1;
		for (int j = 1;j <= i;++j) c[i][j] = (c[i - 1][j - 1] + c[i - 1][j]) % mod;
	}
	for (int i = 1;i <= n;++i) {
		for (int j = 1;j <= K;++j) {
			if (i == 1) f[i][j] = 1;
			else for (int k = 1;k < i;++k) {
				int cur = 1LL * c[i - 2][k - 1] * f[k][j] % mod;
				cur = 1LL * cur * prf[i - k][j - 1] % mod;
				f[i][j] = (f[i][j] + cur) % mod;
			} 
			prf[i][j] = (prf[i][j - 1] + f[i][j]) % mod;
		}
	}
	cout << f[n][K] << '\n';
}