Let $g(a,n,b,m)$ be the smallest non-negative solution $x$ to the system:
$x=amodn$
$x=bmodm$
if such a solution exists, otherwise $0$.

E.g. $g(2,4,4,6)=10$, but $g(3,4,4,6)=0$.

Let $\varphi (n)$ be Euler's totient function.

Let $f(n,m)=g(\varphi (n),n,\varphi (m),m)$

Find $\sum f(n,m)$ for $1000000\le n<m<1005000$.