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;
const int maxn=307;
int n,K,mod;
int C[maxn][maxn];
int f[maxn][maxn];
int s[maxn][maxn];
int main(){
	scanf("%d%d%d",&n,&K,&mod),++n;
	for(int i=0;i<=n;i++){
		C[i][0]=1;
		for(int j=1;j<=i;j++)C[i][j]=(C[i-1][j-1]+C[i-1][j])%mod;
	}
	for(int x=0;x<=K;x++)f[1][x]=1,s[1][x]=K-x+1;
	for(int i=2;i<=n;i++){
		for(int j=0;j<=K;j++){
			for(int k=1;k<i;k++){
				(f[i][j]+=C[i-2][k-1]*1ll*s[k][j+1]%mod*f[i-k][j]%mod)%=mod;
			}
		}
		for(int j=K;j>=0;j--)s[i][j]=(s[i][j+1]+f[i][j])%mod;
	}
	printf("%d\n",f[n][0]);
	return 0;
}

