# Resolution of curve singularity

Let $\pi:X\longrightarrow C$ be the minimal good resolution of the curve singularity $(C,o)$ with exceptional set $E$, where $C:=${$x_1x_2(x_1^{a_1}+x_2^{a_2})=0$}$\subset \mathbb C^2$, $a_1,a_2\geq 2$ are integers. Let $\tilde C_i$ be the strict transform of {$x_i=0$} for $i=1,2$. Why $\tilde C_1$ and $\tilde C_2$ intersect distinct ends of $E$ if $E$ is not irreducible?

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