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;
#define rint register int
inline int read(){int r;int s=0,c;for(;!isdigit(c=getchar());s=c);for(r=c^48;isdigit(c=getchar());(r*=10)+=c^48);return s^45?r:-r;}
int n, K, MOD, f[305][305], C[305][305];
int main()
{
	n = read()+1, K = read(), MOD = read(); for(rint k = 1; k <= K; f[0][k] = 1, k++);
	for(rint i = 0, j; i <= n; i++) for(j = C[i][0] = 1; j <= i; C[i][j] = (C[i-1][j]+C[i-1][j-1])%MOD, j++);
	for(rint i = 1, k, j; i <= n; i++) for(f[i][1] = 1, k = 2; k <= K; k++) for(j = 0; j <= i; j++)
		f[i][k] = (f[i][k]+1ll*C[i-1][j-1]*f[j][k-1]%MOD*f[i-j][k])%MOD; printf("%d\n",f[n][K]); return 0;
}