Higher direct image of morphism with generic fiber $\mathbb{P}^1$

Question

Let $f:X\to Y$ be the morphism of smooth varieties over $\mathbb{C}$ with generic fiber equal to $\mathbb{P}^1$. How to prove that $R^if_*\mathcal{O}_X=0$ for $i>0$?

(I do not need the complete solution, just an idea)