# Practice on Toph

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# Smallest Interval

By Sherlock221b · 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 $N$ ($1 \le N \le 10^5$) and $K$ ($1 \le K \le N$). The next line consists of $N$ space separated integers denoting Alice's numbers. Let, $a^i$ ($1 \le a_i \le 10^9$) be the $i^{th}$ number on this line.

## 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


The desired interval is [4,8] which contains 4, 5 and 8. The size of this interval is 4.

InputOutput
6 2
16 5 7 4 4 8

0


The desired interval is [4,4] which contains 4 and 4. The size of this interval is 0.

### Statistics

85% Solution Ratio

ArpancseEarliest, May '17

Tarik.amtolyFastest, 0.0s

ArpancseLightest, 524 kB

Rafi9998Shortest, 210B