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 <cstring>
#include <algorithm>
#define fo(i,a,b) for(int i=a;i<=b;i++)
#define fd(i,a,b) for(int i=a;i>=b;i--)
using namespace std;

typedef long long ll;

const int N=305;

int n,k,Mo,f[N][N],C[N][N],s[N][N];

int main() {
	scanf("%d%d%d",&n,&k,&Mo);
	fo(i,0,n) {
		C[i][0]=1;
		fo(j,1,i) C[i][j]=(C[i-1][j]+C[i-1][j-1])%Mo;
	}
	fo(i,0,k) f[1][i]=1,s[1][i]=k-i+1;
	fo(i,2,n+1) {
		fo(j,0,k)
			fo(l,1,i-1)
				(f[i][j]+=(ll)f[i-l][j]*s[l][j+1]%Mo*C[i-2][l-1]%Mo)%=Mo;
		fd(j,k,0) s[i][j]=(s[i][j+1]+f[i][j])%Mo;
	}
	printf("%d\n",f[n+1][0]);
	return 0;
}