Reactor Fuel Rod Batch Trim Minimum

A reactor facility stores fuel rods that must be packaged in batches: a batch is only accepted for storage if the total remaining length of all its rods is exactly divisible by the facility's required batch size k. You are given the current lengths of n fuel rods. In one operation, you may select any single rod and trim exactly 1 unit off its length (a rod's length may be trimmed all the way down to 0). Determine the minimum number of trim operations needed so that the sum of all rod lengths becomes divisible by k.

Input format

The first line contains two integers n and k. The second line contains n integers, the lengths of the rods.

Output format

Print a single integer: the minimum number of trim operations required.

Constraints

• 1 <= n <= 100000
• 1 <= k <= 10^9
• 1 <= rod length <= 10^9

3 5
3 7 10

0

3 4
1 2 3

2