KöMaL 2023 B5299

There is a flea sitting at each of points $1,2,3$ of the number line. If one flea is at point $a$ and another is at point $b$, then the flea at $a$ may jump to the point $2b-a$. Is it possible for the fleas to end up at points $2^{100},3^{100},2^{100}+3^{100}$ with a finite sequence of such steps?