### Problem Statement

n children walk around a circle with n-1 evenly-spaced chairs. When the music stops, each one tries to get to the nearest chair. One of them is bound to fail thus providing a lesson about life. We want to identify the loser.

The children start evenly spaced around the circle, with the first child, A, located right next to a chair. The child who follows A as they walk around the circle is B, the one who follows B is C, etc. The children all start walking when the music starts at a speed that will get them all the way around the circle in 10 seconds. When the music stops, they each try to get to the nearest chair.

Create a class Musical that contains a method loser that is given n (the number of children) and time (the number of seconds the music plays). The method should return the name of the loser as a String containing just one uppercase letter.

It may be helpful to note that the child who is farther from any chair than each other child is always the loser.

### Definition

 Class: Musical Method: loser Parameters: int, double Returns: String Method signature: String loser(int n, double time) (be sure your method is public)

### Constraints

-n will be between 2 and 26 inclusive.
-time will be between 1.0 and 100.0 inclusive.
-For all values within 1.0 E-9 of time the same child would be the loser.

### Examples

0)

 `3` `1.2`
`Returns: "B"`
 Starting from their original positions they walk for 1.2 seconds. When the music stops the closest chair to A is the first chair, the one he started at. Meanwhile B has moved to the point where now that chair is also the closest chair for him. But A is closer than B so B is the loser. (C is closest to the second chair and has no competition for that one.)
1)

 `3` `12.0`
`Returns: "A"`
 The children walk all the way around the circle and a little farther before the music stops. The situation is almost the same now as in the previous case, with A and B racing for the first chair, but this time A is farther away than B.
2)

 `26` `100.0`
`Returns: "N"`
3)

 `2` `15.0`
`Returns: "A"`
 The 2 children start out with A next to the chair and B on the other side of the circle. After 15 seconds, they have gone around the circle one and a half times, so B is next to the chair and A is the loser.

#### Problem url:

http://www.topcoder.com/stat?c=problem_statement&pm=4495

#### Problem stats url:

http://www.topcoder.com/tc?module=ProblemDetail&rd=7222&pm=4495

dgoodman

#### Testers:

PabloGilberto , lbackstrom , brett1479

Math