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;
int n,k,mod;
int C[305][305];
int f[305][305];
int s[305][305];

int main(){
	cin>>n>>k>>mod;
	C[0][0]=1;
	for(int i=1;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 j=0;j<=k;j++) f[1][j]=1,s[1][j]=k-j+1; 
	for(int i=2;i<=n+1;i++){
		for(int j=0;j<=k;j++){
			for(int u=1;u<i;u++) (f[i][j]+=1ll*C[i-2][u-1]*f[i-u][j]%mod*s[u][j+1]%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+1][0]);

	return 0;
}