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.

Examples

Input

2 2 100


Output

5


Input

4 3 999999999


Output

358


Input

150 150 998244353


Output

186248260
#include <cstdio>
#include <iostream>
#include <cstring>
using namespace std;
typedef long long ll;
const int N = 300+10;
ll f[N][N][N];
int n,k,m;
void add(ll &a,ll b) {a=(ll)(a+b)%m;}
int main() {
	cin>>n>>k>>m;
	f[0][1][0] = 1;
	for (int i = 0; i <= n; i++) {
		for (int j = 1; j <= k; j++) {
			for (int k = i; ~k; k--) {
				if (k) add(f[i][j][k-1],f[i][j][k]);
				add(f[i+1][j][k],f[i][j][k] * (k+1));
			}
			add(f[i][j+1][i], f[i][j][0]);
		}
	}
	cout<<f[n][k][0]<<endl;
}