For a school of 250 students, a leader is to be chosen. Principal asks them to stand in a circle, as per their roll numbers from 1 to 250 in clockwise direction, such that number 250 is standing near number 1 to compete the circle. Starting from number 1, every student loudly declares the roll number of student standing next to him in clockwise direction. Immediately after such declaration, the student whose roll number is declared is removed from the circle. The game continues with next available student in the circle, who loudly declares the roll number of next available student, till only 1 student remains in the circle. For example, at start, roll number 1 loudly declares the roll number 2, who is available immediately next to him in clockwise direction. So number 2 is removed from the circle. Next student available is roll number 3, who declares roll number 4, and so on. This continues till only one student remains, who is declared as the leader.
Can you tell, who is going to be the leader of this class?

Can you come up with a general formula to identify the winner for N number of students?