Christmas Eve

In some other world, today is Christmas Eve.

There are N trees planted in Mr. Takaha's garden. The height of the i-th tree (1 \leq i \leq N) is h_i meters.

He decides to choose K trees from these trees and decorate them with electric lights. To make the scenery more beautiful, the heights of the decorated trees should be as close to each other as possible.

More specifically, let the height of the tallest decorated tree be h_{max} meters, and the height of the shortest decorated tree be h_{min} meters. The smaller the value h_{max} - h_{min} is, the better. What is the minimum possible value of h_{max} - h_{min}?

Constraints

• 2 \leq K < N \leq 10^5
• 1 \leq h_i \leq 10^9
• h_i is an integer.

Input

Input is given from Standard Input in the following format:

N K h_1 h_2 : h_N

Output

Print the minimum possible value of h_{max} - h_{min}.

Examples

Input

5 3 10 15 11 14 12

Output

2

Input

5 3 5 7 5 7 7

Output

0

inputFormat

Input

Input is given from Standard Input in the following format:

N K h_1 h_2 : h_N

outputFormat

Output

Print the minimum possible value of h_{max} - h_{min}.

Examples

Input

5 3 10 15 11 14 12

Output

2

Input

5 3 5 7 5 7 7

Output

0

样例

5 3
10
15
11
14
12

2