Using RSA: we know N, two public exponents ($e_1$ and $e_2$) and two secret exponents ($d_1$ and $d_2$). Find primes p and q if $N=pq$.
We know: $\gcd(e_1,(p-1)(q-1))=1$, $\gcd(e_2,(p-1)(q-1))=1$, $e_1d_1\equiv 1$ and $e_2d_2\equiv 1$ mod$(p-1)(q-1)$. We also get the hint $\gcd(e_1d_1-1,e_2d_2-1)=b$, where b is known.
Assuming we know $e_1,e_2,d_1,d_2,N, b$, how do I find p and q? I tried to rewrite some congruences but got nowhere.