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<algorithm>
#include<iostream>
#include<iomanip>
#include<cstring>
#include<cstdio>
using namespace std;
#define ll long long
ll n,m,mod,f[305][305][305];
#define add(x) (x>=mod?x-mod:x)
int main(){
	scanf("%lld%lld%lld",&n,&m,&mod);
	f[0][1][0]=1;
	for(ll i=0;i<=n;i++){
		for(ll t=1;t<=m;t++){
			for(ll j=i;j>=0;j--){
				if(j) f[i][t][j-1]=add(f[i][t][j-1]+f[i][t][j]);
				else f[i][t+1][i]=add(f[i][t+1][i]+f[i][t][j]);
				f[i+1][t][j]=(f[i+1][t][j]+f[i][t][j]*(j+1))%mod;
			}
		}
	}
	printf("%lld",f[n][m][0]);
}