Unique-neighbor expander


I want to solve Problem 4.10 from Randomness by Salil Vadhan. https://people.seas.harvard.edu/~salil/cs225/spring15/PS3.pdf

Consider a bipartite expander $ G$ with left degree $ D$ so that every subset $ S$ of the left vertices with at most $ K$ vertices has at least $ (1-\epsilon)D|S|$ neighbors. Then $ G$ also has the property that it has $ (1-2\epsilon)D|S|$ unique neighbors. Unique meaning that it has exactly one corresponding vertex from $ S$ .

I recognize that the new expansion factor is $ (1-2\epsilon)D = 2\cdot(1-\epsilon)D -D$