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>
typedef long long ll;
ll gi(){
	ll x=0,f=1;
	char ch=getchar();
	while(!isdigit(ch))f^=ch=='-',ch=getchar();
	while(isdigit(ch))x=x*10+ch-'0',ch=getchar();
	return f?x:-x;
}
int f[310][310],sf[310][310],C[310][310];
int main(){
#ifdef XZZSB
	freopen("in.in","r",stdin);
	freopen("out.out","w",stdout);
#endif
	int n=gi(),k=gi()+1,mod=gi();
	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 i=1;i<=k;++i)f[1][i]=1,sf[1][i]=k-i+1;
	for(int i=2;i<=n+1;++i)
		for(int j=k;j;--j){
			for(int o=1;o<i;++o)f[i][j]=(f[i][j]+1ll*C[i-2][o-1]*f[i-o][j]%mod*sf[o][j+1])%mod;
			sf[i][j]=(f[i][j]+sf[i][j+1])%mod;
		}
	printf("%d\n",f[n+1][1]);
	return 0;
}
