CONO-SUR 1996 Problem 5

We want to cover totally a square(side is equal to $k$ integer and $k>1$ ) with this rectangles: $1$ rectangle ( $1\times 1$ ), $2$ rectangles ( $2\times 1$ ), $4$ rectangles ( $3\times 1$ ),...., $2^n$ rectangles ( $n + 1 \times 1$ ), such that the rectangles can't overlap and don't exceed the limits of square. Find all $k$ , such that this is possible and for each $k$ found you have to draw a solution