TH-TMO 2022 Problem 3

Let $\Omega$ be a circle in a plane. $2022$ pink points and $2565$ blue points are placed inside $\Omega$ such that no point has two colors and no two points are collinear with the center of $\Omega$ . Prove that there exists a sector of $\Omega$ such that the angle at the center is acute and the number of blue points inside the sector is greater than the number of pink points by exactly $100$ . (Note: such sector may contain no pink points.)