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 rep(i,x,y) for (int i=(x);i<=(y);i++)
#define per(i,x,y) for (int i=(x);i>=(y);i--)
#define ll long long
#define inf 1000000001
using namespace std;
#define N 305
int n,K,mod,f[N][N],s[N][N],C[N][N];
void init(int n){
	rep (i,0,n) C[i][0]=1;
	rep (i,1,n) rep (j,1,i) C[i][j]=(C[i-1][j-1]+C[i-1][j])%mod;
}
void upd(int &x,int y){x+=y;x-=x>=mod?mod:0;}
int main(){
	cin>>n>>K>>mod;init(n);n++;
	rep (i,0,K) f[1][i]=1;
	per (i,K,0) s[1][i]=(s[1][i+1]+1)%mod;
	/*f[n][x]+=f[n-k][x]*f[k][y]*C(n-2,k-1);(y--->x)y>x*/
	rep (i,2,n){
		rep (j,0,K) rep (k,1,i-1) upd(f[i][j],(ll)f[i-k][j]*s[k][j+1]%mod*C[i-2][k-1]%mod);
		per (j,K,0) s[i][j]=(s[i][j+1]+f[i][j])%mod;
	}
	cout<<f[n][0]<<'\n';
	return 0;
}