Rows

You are given a matrix $B$ of size $N \times K$, i.e. $N$ rows and $K$ columns. $B_{(i, j)}$ denotes the value in the cell $(i, j)$. You can buy the $i$-th row of the matrix for $A_i$ coins. Your goal is to buy a non-empty subset of the rows, and then create a set with $K$ cells such that the set has exactly one cell from each column; but you are restricted to pick cells only from the rows that