Let $a$, $b$, $p$, and $q$ be fixed positive integers. If an $a\times b$ grid can be tiled using some $1\times p$ and $q\times 1$ pieces, show that either $a$ is divisible by $p$ or $b$ is divisible by $q$. Here, a $1\times k$ and $k\times 1$ grids are treated as different.