Suppose we have an oracle which works as follows: We can give it a graph which has been partially k$-$colored $($meaning some but not all over the vertices have been k$-$colored$)$ and it tells us whether it is possible to complete the k$-$coloring to the entire graph. Now suppose a graph can be k$-$colored. Explain why the k$-$coloring problem is polynomially reducible to the oracle.