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Chocolate Distribution

1. Given an array A[] of positive integers of size N, where each value represents the number of chocolates in a packet. Each packet can have a variable number of chocolates. There are M students, the task is to distribute chocolate packets among M students such that : 2. Each student gets exactly one packet. 3. The difference between maximum number of chocolates given to a student and minimum number of chocolates given to a student is minimum.

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Chocolate Distribution

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1. Given an array A[] of positive integers of size N, where each value represents the number of chocolates in a packet. Each packet can have a variable number of chocolates. There are M students, the task is to distribute chocolate packets among M students such that : 2. Each student gets exactly one packet. 3. The difference between maximum number of chocolates given to a student and minimum number of chocolates given to a student is minimum.

Constraints

1 <= N <= 10^5 1 <= Ai <= 10^9 1 <= M <= N

Format

Input

Input is managed for you

Output

Output is managed for you

Example

Sample Input

8 3 4 1 9 56 7 9 12 5

Sample Output

6

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