Given natural numbers $p < k < n$. On an endless checkered plane some cells are marked so that in any rectangle $(k + 1) \times n$ ($n$ cells horizontally, $k + 1$ vertically) marked exactly $p$ cells. Prove that there is a $k \times (n + 1)$ rectangle ($n + 1$ cell horizontally, $k$ - vertically), in which no less than $p + 1$ cells.