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: Wrong Answer)

//21
#include<cstdio>
#include<algorithm>
using namespace std;

const int maxn = 301;

int n, k, lbt;
int dp[maxn][maxn], sdp[maxn][maxn];
int c[maxn][maxn];
int ans[maxn];

int main() {
	scanf("%d%d%d", &n, &k, &lbt);
	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] + c[i - 1][j - 1]) % lbt;
		}
	}
	for (int j = 1; j <= k + 1; j++) {
		dp[1][j] = 1;
		sdp[1][j] = j % lbt;
	}
	for (int len = 2; len <= n; len++) {
		for (int j = 1; j <= k; j++) {
			for (int i = 1; i < len; i++) {
				dp[len][j] = (dp[len][j] + (long long)c[len - 2][i - 1] * sdp[i][j - 1] % lbt * dp[len - i][j]) % lbt;
			}
			sdp[len][j] = (sdp[len][j - 1] + dp[len][j]) % lbt;
		}
	}
	ans[0] = 1;
	for (int len = 1; len <= n; len++) {
		for (int i = 1; i <= len; i++) {
			ans[len] = (ans[len] + (long long)c[len - 1][i - 1] * sdp[i][k] % lbt * ans[len - i]) % lbt;
		}
	}
	printf("%d", ans[n]);
	return 0;
}