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<bits/stdc++.h>
using namespace std;

const int N = 305;
typedef long long LL;

int n, m;
LL ans, mod, f[N][N], suf[N][N], c[N][N];

int main() {
	cin>>n>>m>>mod;
	c[0][0] = 1;
	for(int i = 1; i <= max(n, m); i++) {
		c[i][0] = 1;
		for(int j = 1; j <= i; j++)
		    c[i][j] = (c[i - 1][j - 1] + c[i - 1][j])%mod; 
	}
	for(int i = 0; i <= m; i++) 
		f[1][i] = 1, suf[1][i] = m - i + 1;
	for(int i = 2; i <= n + 1; i++) {
		for(int j = m; j >= 0; j--) {
			for(int k = 1; k < i; k++)
				f[i][j] = (f[i][j] + c[i - 2][k - 1]*f[i - k][j]%mod*suf[k][j + 1])%mod;
			suf[i][j] = (suf[i][j + 1] + f[i][j])%mod;
		}
	}
	cout<<f[n + 1][0]<<endl;
	return 0;
}