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;

int N , K , M , C[303][303] , f[303][303] , sum[303][303]; bool visf[303][303] , vissum[303][303];

int getf(int , int);
int getsum(int , int);

int main(){
	cin >> N >> K >> M;
	for(int i = 0 ; i <= N ; ++i){
		C[i][0] = 1;
		for(int j = 1 ; j <= i ; ++j)
			C[i][j] = (C[i - 1][j] + C[i - 1][j - 1]) % M;
	}
	cout << getf(N + 1 , 0) << endl; return 0;
}

int getf(int x , int y){
	if(y > K) return 0;
	if(visf[x][y]) return f[x][y];
	visf[x][y] = 1; if(x == 1) return f[x][y] = 1;
	for(int i = 1 ; i < x ; ++i)
		f[x][y] = (f[x][y] + 1ll * C[x - 2][i - 1] * getf(x - i , y) % M * getsum(i , y + 1)) % M;
	return f[x][y];
}

int getsum(int x , int y){
	if(y > K) return 0;
	if(vissum[x][y]) return sum[x][y];
	vissum[x][y] = 1; return sum[x][y] = (getsum(x , y + 1) + getf(x , y)) % M;
}