An error in applying Riemann-Hurwitz formula?

Question

I did try to compute the genus of a curve of bidegree $(a,b)$ in $\mathbb P ^1 \times \mathbb P^1$. I did choose the curve $X = \{ x_0^ay_0^b = x_1^ay_1^b\}$. Consider the projection to the $x$ component $\pi : X \to \mathbb P^1$. This is a degree $b$ map with two ramifications points ($0$ and $\infty$), both of index $b-1$. Thus I get $\chi(X) = 2b - 2(b-1) = 2$ which is obviously false. I know the correct answer is $(a-1)(b-1)$. Where is my mistake ? Thanks in advance.