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 gc getchar()
using namespace std;
typedef long long ll;
const int N=309;
int n,m,mod,C[N][N],f[N][N],g[N][N];
int read()
{
	int x=1;
	char ch;
	while (ch=gc,ch<'0'||ch>'9') if (ch=='-') x=-1;
	int s=ch-'0';
	while (ch=gc,ch>='0'&&ch<='9') s=s*10+ch-'0';
	return s*x;
}
int main()
{
	n=read(),m=read(),mod=read();
	C[0][0]=1;
	for (int i=1;i<N;i++)
		for (int j=0;j<=i;j++) C[i][j]=(C[i-1][j]+(j?C[i-1][j-1]:0))%mod;
	for (int i=0;i<=m;i++) f[1][i]=1,g[1][i]=m-i+1;
	for (int i=2;i<=n+1;i++)
		for (int j=0;j<=m;j++)
		{
			for (int k=1;k<i;k++)
				f[i][j]=(f[i][j]+(ll)C[i-2][k-1]*f[i-k][j]%mod*g[k][j+1])%mod;
			for (int k=1;k<=j;k++) g[i][k]=(g[i][k]+f[i][j])%mod;
		}
	printf("%d\n",f[n+1][0]);
	return 0;
}
