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 <iostream>
#include <cstdio>
#include <cstdlib>
#include <cstring> 
#include <cmath> 
#include <algorithm> 
using namespace std; 
const int MAX_N = 305;
int N, K, Mod; 
int C[MAX_N][MAX_N], f[MAX_N][MAX_N], sum[MAX_N][MAX_N]; 

int main () { 
	cin >> N >> K >> Mod; 
	for (int i = 0; i <= N; i++) { 
		C[i][0] = C[i][i] = 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 <= K; i++) f[1][i] = 1, sum[1][i] = K - i + 1; 
	for (int i = 2; i <= N + 1; i++) { 
		for (int j = 0; j <= K; j++) 
			for (int k = 1; k < i; k++) 
				f[i][j] = (f[i][j] + 1ll * f[i - k][j] * sum[k][j + 1] % Mod * C[i - 2][k - 1]) % Mod; 
		for (int j = K; ~j; j--) sum[i][j] = (f[i][j] + sum[i][j + 1]) % Mod; 
	} 
	printf("%d\n", f[N + 1][0]); 
    return 0; 
} 