You are given an array of positive integers price where price[i] denotes the price of the ith candy and a positive integer k.

The store sells baskets of k distinct candies. The tastiness of a candy basket is the smallest absolute difference of the prices of any two candies in the basket.

Return the maximum tastiness of a candy basket.

 

Example 1:

Input: price = [13,5,1,8,21,2], k = 3
Output: 8
Explanation: Choose the candies with the prices [13,5,21].
The tastiness of the candy basket is: min(|13 - 5|, |13 - 21|, |5 - 21|) = min(8, 8, 16) = 8.
It can be proven that 8 is the maximum tastiness that can be achieved.

Example 2:

Input: price = [1,3,1], k = 2
Output: 2
Explanation: Choose the candies with the prices [1,3].
The tastiness of the candy basket is: min(|1 - 3|) = min(2) = 2.
It can be proven that 2 is the maximum tastiness that can be achieved.

Example 3:

Input: price = [7,7,7,7], k = 2
Output: 0
Explanation: Choosing any two distinct candies from the candies we have will result in a tastiness of 0.

 

Constraints:

• 2 <= k <= price.length <= 105
• 1 <= price[i] <= 109