Seating

PROBLEM STATEMENT

At the recent TopCoder Invitational, an effort was made to seat diners at the
awards banquet so that the staff and the competitors mingled as much as
possible.

Given m members and n staffers, to be assigned to k tables each seating r
people, you are to find the "best" seating arrangement according to a certain
metric.  Define the "imbalance" at a table as the difference between the number
of staffers seated there and the number of members seated there.  So a table
with 9 staffers and no room for anyone else has an imbalance of 9, and a table
with 5 members and 4 staffers has an imbalance of 1.  Empty tables have an
imbalance of 0, naturally.  Define the "overall imbalance" of a seating
arrangement as the worst (greatest) imbalance at any one table.

Find the assignment with the minimum possible overall imbalance, and return the
imbalance.  Your method will be called with the four values listed above.  If
you cannot find *any* arrangement, that is, there are not enough seats for
everyone, return -1.  Tables may be left partially or completely empty.

DEFINITION

Class Name: Seating
Method Name: best
Parameters: int, int, int, int
Returns: int

Here is the method signature (make sure your method is public): int best(int m,
int n, int k, int r);

TopCoder will ensure that m, n, k, and r will all be between 0 and 1000,
inclusive.

EXAMPLES
best(9, 0, 1, 9) = 9
best(4, 5, 1, 30) = 1
best(1, 0, 3, 4) = 1
best(8, 8, 6, 6) = 0
best(8, 8, 6, 3) = 1
best(12, 8, 6, 6) = 1
best(12, 8, 2, 10) = 2
best(300, 50, 7, 50) = 36
best(20, 20, 4, 8) = -1