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