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 
using namespace std;
const int maxn=310;
int mod,n,K;
ll dp[maxn][maxn],C[maxn][maxn],sum[maxn][maxn];
void wo(int x) {
	for(int i=K;i>=0;i--) sum[x][i]=(sum[x][i+1]+dp[x][i])%mod; 
}
int main() 
{
	scanf("%d%d%d",&n,&K,&mod);
	C[0][0]=1;
	for(int i=1;i<=n+1;++i) {C[i][0]=1;
		for(int j=1;j<=i;++j) C[i][j]=(C[i-1][j]+C[i-1][j-1])%mod; 
	}
	for(int i=0;i<=K;++i) dp[1][i]=1;
	wo(1);
	for(int i=2;i<=n+1;++i) {
		for(int j=0;j<=K;++j) {
			for(int k=1;k<i;++k) {
				dp[i][j]=(dp[i][j]+sum[k][j+1]*dp[i-k][j]%mod*C[i-2][k-1]%mod)%mod;		
			}
		}
		wo(i);
	}
	cout<<dp[n+1][0]<<"\n";
	return 0;
} 
