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;

int n,k,mo,f[305][305],g[305][305],C[305][305];

void work()
{
	scanf("%d %d %d",&n,&k,&mo);
	for (int i=0; i<=300; i++)
		{
			C[i][0]=1;
			for (int j=1; j<=i; j++)
				C[i][j]=(C[i-1][j-1]+C[i-1][j])%mo;
		}
	for (int i=1; i<=k; i++)  f[1][i]=1,g[1][i]=i%mo,g[0][i]=1;
	for (int i=2; i<=n; i++)
		{
			for (int j=1; j<=k; j++)
				f[i][j]=g[i-1][j-1];
			for (int j=1; j<=i; j++)
				{
					int s=0;
					for (int l=1; l<=k; l++)
						s=(s+f[j][l])%mo,g[i][l]=(g[i][l]+1LL*g[i-j][l]*s%mo*C[i-1][j-1])%mo;
				}
		}
	printf("%d",g[n][k]);
}

int main()
{
	work();
	return 0;
}