PL-OM 2023 Problem 2

Given an acute triangle $ABC$ with their incenter $I$ . Point $X$ lies on $BC$ on the same side as $B$ wrt $AI$ . Point $Y$ lies on the shorter arc $AB$ of the circumcircle $ABC$ . It is given that $$\angle AIX = \angle XYA = 120^\circ.$$ Prove that $YI$ is the angle bisector of $XYA$ .