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 N 310
using namespace std;
template <typename T> void read(T &x){
	x=0;char ch=getchar();int fh=1;
	while (ch<'0'||ch>'9'){if (ch=='-')fh=-1;ch=getchar();}
	while (ch>='0'&&ch<='9')x=x*10+ch-'0',ch=getchar();
	x*=fh;
}
int n,c,mo;
ll da[N][N],dp[N][N],C[N][N];
int main(){
	cin>>n>>c>>mo;
	C[0][0]=1;
	for (int i=1;i<=300;i++)
		for (int j=0;j<=i;j++){C[i][j]=C[i-1][j];if (j)C[i][j]=(C[i][j]+C[i-1][j-1])%mo;}
	for (int i=0;i<=c;i++)dp[1][i]=1,da[1][i]=c-i+1;
	for (int i=2;i<=n+1;i++){
		for (int j=c;j>=0;j--)
			for (int k=1;k<i;k++)
				dp[i][j]=(dp[i][j]+(dp[i-k][j]*da[k][j+1]%mo)*C[i-2][k-1])%mo;
		for (int j=c;j>=0;j--)da[i][j]=(dp[i][j]+da[i][j+1])%mo;
	}
	cout<<dp[n+1][0]<<endl;
	return 0;
}