Minimum Difference Subset

You are given an array of n integers and an integer K. Your task is to select any K elements from the array such that the difference between the maximum and minimum of these selected elements is minimized.

In other words, if after selecting and then sorting the K elements you obtain an array a, you need to minimize the value

$$\min_{0 \le i \le n-K} (a[i+K-1]-a[i])$$

Note: The chosen elements do not need to be consecutive in the original array. You can choose any K elements.

Example:

Input: 6 3
       1 3 6 4 1 2
After selecting and sorting a possible subset [1,1,2], the difference is 2-1 = 1.
Output: 1

inputFormat

The first line contains two integers n and K separated by a space, where n is the number of elements in the array. The second line contains n integers separated by spaces representing the array.

\(1 \leq K \leq n\)

outputFormat

Output a single integer: the minimum absolute difference between the maximum and minimum among any chosen subset of K elements.

## sample

6 3
1 3 6 4 1 2

1

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