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 <cctype>
#include <algorithm>
#include <cstring>
#include <map>
#include <vector>
#include <queue>
#define fi first
#define se second
using namespace std;
typedef long long i64;
typedef pair<int, i64> pii;
inline int read(int f = 1, int x = 0, char ch = ' ')
{
    while(!isdigit(ch = getchar())) if(ch == '-') f = -1;
    while(isdigit(ch)) x = x*10+ch-'0', ch = getchar();
    return f*x;
}
const int N = 3e2+5;
int n, k, P, f[N][N][N];
int main()
{
	n = read(), k = read(), P = read();
	f[0][1][0] = 1;
	for(int i = 0; i <= n; ++i)
		for(int j = 1; j <= k; ++j)
			for(int p = i; ~p; --p)
			{
				if(p) f[i][j][p-1] = (f[i][j][p-1]+f[i][j][p])%P;
				else f[i][j+1][i] = (f[i][j+1][i]+f[i][j][p])%P;
				f[i+1][j][p] = (f[i+1][j][p]+(1ll+p)*f[i][j][p])%P;
			}
	printf("%d\n", f[n][k+1][n]);
	return 0;
}