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>
#define ll long long
#define ull unsigned ll
#define uint unsigned
#define pii pair<int,int>
#define pll pair<ll,ll>
#define PB push_back
#define fi first
#define se second
#define For(i,j,k) for (int i=(int)(j);i<=(int)(k);i++)
#define Rep(i,j,k) for (int i=(int)(j);i>=(int)(k);i--)
#define CLR(a,v) memset(a,v,sizeof(a));
#define CPY(a,b) memcpy(a,b,sizeof(a));
using namespace std;
const int N=305;
int n,K,mo;
int C[N][N],f[N][N],S[N][N];
int main(){
	scanf("%d%d%d",&n,&K,&mo);
	For(i,0,N-1) C[i][0]=1;
	For(i,1,N-1) For(j,1,i)
		C[i][j]=(C[i-1][j]+C[i-1][j-1])%mo;
	For(i,0,K){
		f[1][i]=1;
		S[1][i]=K-i+1;
	}
	For(i,2,n+1){
		For(j,1,i-1) For(k,0,K)
			f[i][k]=(f[i][k]+1ll*f[i-j][k]*S[j][k+1]%mo*C[i-2][j-1])%mo;
		Rep(j,K,0) S[i][j]=(S[i][j+1]+f[i][j])%mo;
	}
	printf("%d\n",f[n+1][0]);
}