Poster Perimeter

Chef wants to print out a poster on a **rectangular** piece of paper. The piece of paper he uses cannot be too large, or his printer will be unable to handle it. Specifically, the length of the rectangle must be an *integer* between $1$ and $N$ units, and the width must be an *integer* between $1$ and $M$ units. Chef would like it if the perimeter of the paper is as close to $K$ as possible.