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<cstdio>
#define N 303
#define ll long long
int c[N][N],f[N][N],g[N][N],i,j,k,l,m,n;
inline int mod(int x){return x<m?x:x-m;}
int main()
{
    scanf("%d%d%d",&n,&l,&m);
    for(i=0;i<=l;i++)f[1][i]=1,g[1][i]=(l-i+1)%m;
    for(i=0;i<=n;i++)for(j=*c[i]=1;j<=i;j++)c[i][j]=mod(c[i-1][j-1]+c[i-1][j]);
    for(i=2;i<=n+1;i++)for(j=l;j--;g[i][j]=mod(g[i][j+1]+f[i][j]))for(k=1;k<i;k++)f[i][j]=(f[i][j]+(ll)f[i-k][j]*g[k][j+1]%m*c[i-2][k-1])%m;
    return 0&printf("%d\n",f[n+1][0]);
}