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++ (GCC 9.2.1) (judge verdict: Accepted)

#include<bits/stdc++.h>
using namespace std;
int n,m,p,f[310][310][310];
//f[i][j][k]:we've finished constructing the first i sequences, now we're going to add the number j into the i+1-th sqeuence, and there're k places to add j into
int main(){
	scanf("%d%d%d",&n,&m,&p),f[0][1][0]=1;
	for(int i=0;i<=n;i++)for(int j=1;j<=m;j++)for(int k=i;k>=0;k--){
		if(k)(f[i][j][k-1]+=f[i][j][k])%=p;//we decide not to add j to the k-th place, so we could add it to the (k-1)-th place.
		else(f[i][j+1][i]+=f[i][j][k])%=p;//we have tried every place j could be added to, now it's time to try j+1, which could be added into any place
		(f[i+1][j][k]+=1ll*f[i][j][k]*(k+1)%p)%=p;//we decide to add j to the k-th place, and there are (k+1) places for us to add (including the last one)
	}
	printf("%d\n",f[n][m+1][n]);//all n sequences've been constructed, and all number've been tried
	return 0;
}