Practice on Toph

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Smallest Interval

Limits: 1s, 512 MB

Alice has a collection of N numbers. She would like to place them on a number line. She places each of the N numbers on the point corresponding to its value on the number line. Now she wonders, what’s the size of the smallest interval on the number line such that there are at least K numbers from her collection on that interval?

Input

The first line of the input contains two integers N and K. The next line consists of N space separated integers denoting Alice’s numbers. Let, ai be the ith number on this line.

Constraints:

1 ≤ N ≤ 105

1 ≤ K ≤ N

1 ≤ ai ≤ 109

Output

In a single line, print the size of the smallest interval on the number line where at least K integers from Alice’s collection can be found.

Samples

InputOutput
5 3
17 12 5 4 8 
4
6 2
16 5 7 4 4 8 
0

Explanation of Sample Case 1: The desired interval is [4,8] which contains 4, 5 and 8. The size of this interval is 4.

Explanation of Sample Case 2: The desired interval is [4,4] which contains 4 and 4. The size of this interval is 0.

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