Solve the following exercise by means of a reduction to SAT:

• A company must complete $m$ different tasks. There are $n$ workers, each of which can perform a subset of the tasks. We want to find a set of exactly $k$ workers, with $k<n$, such that every task can be performed by at least one of the workers of the set.

The input of the exercise and the output with the solution (when the input is solvable) are as follows:

• n: int
  m: int
  k: int
  tasks: array of array of int
  

  The input consists of the naturals $n$, $m$, $k$, and for each task the list indicating which workers can perform it in tasks. The position $(i,j)$ of tasks contains a $1$ if the worker $j$ can perform the task $i$, or $0$ otherwise. The tasks are identified by numbers between $0$ and $m-1$. Similarly, the workers are identified by numbers between $0$ and $n-1$.

• set: array of int
  

  The output is a list containing the identifiers of the workers that are part of the set.