IN-TST 2003 Problem 5

On the real number line, paint red all points that correspond to integers of the form $81x+100y$ , where $x$ and $y$ are positive integers. Paint the remaining integer point blue. Find a point $P$ on the line such that, for every integer point $T$ , the reflection of $T$ with respect to $P$ is an integer point of a different colour than $T$ .