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<iostream>
#include<cstdio>
#define ll long long
using namespace std;
const int maxn=305;
int n,k,m,f[maxn][maxn],C[maxn][maxn],g[maxn][maxn];
inline int add(int x,int y){ x+=y; return x>=m?x-m:x;}
inline void ADD(int &x,int y){ x+=y; if(x>=m) x-=m;}

inline void solve(){
	const int ha=m;
	
	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]=add(C[i-1][j-1],C[i-1][j]);
	}
	
	fill(g[0],g[0]+k+1,1);
	for(int i=0;i<=k;i++) g[1][i]=k-i+1,f[1][i]=1;
	
	for(int i=2;i<=n;i++){
		// calc f[i][]
		
		for(int j=0;j<=k;j++)
		    for(int u=1;u<i;u++) ADD(f[i][j],C[i-2][u-1]*(ll)g[u][j+1]%ha*(ll)f[i-u][j]%ha);
		
		// prepare prefix sum
		
		for(int j=k;j>=0;j--) g[i][j]=add(f[i][j],g[i][j+1]);
	} 
}

int main(){
	scanf("%d%d%d",&n,&k,&m),n++;
	solve(),printf("%d\n",f[n][0]);
	return 0;
}