Candy Distribution Problem

Candy Distribution Puzzle
MathematicsMedium

A group of students are sitting in a circle with the teacher in the center. They all have an even number of candies (not necessarily equal). When the teacher blows a whistle, each student passes half their candies to the student on their left. Then the students who have an odd number of candies get an extra candy from the teacher.

Would all the students ever have the same number of candies after a finite number of whistles?