IN-TST 2009 Problem 2

Let us consider a simle graph with vertex set $V$ . All ordered pair $(a,b)$ of integers with $gcd(a,b) = 1$ , are elements of V. $(a,b)$ is connected to $(a,b + kab)$ by an edge and to $(a + kab,b)$ by another edge for all integer k. Prove that for all $(a,b)\in V$ , there exists a path fromm $(1,1)$ to $(a,b)$ .