A. Minimize Sour Difference
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Alice has $$$n$$$ sour candies, each with some sourness described by an integer. Because she does not like the sourness of her candies to vary too much, she is going to choose $$$k$$$ sour candies and eat them. Alice wants to choose candies to eat in order to minimize the largest (absolute) difference between two candies. If Alice optimally chooses which candies to eat, what is the smallest maximum difference between any two remaining candies?

Input

The first line will contain integers $$$n$$$ and $$$k$$$, ($$$1 \leq k \lt n \leq 1000$$$). The second line will contain $$$n$$$ integers, describing the sourness of the i-th candy.

Output

Output the minimal largest absolute difference between any two candies left. If there is 1 candy left, the answer is 0.

Examples
Input
6 3
1 4 8 9 12 16
Output
4
Input
4 1
2 9 3 1
Output
2
Input
6 4
10 8 2 6 7 10
Output
0
Note

In the first test case, Alice should eat candies with sourness 1, 4, and 16. Then the maximum difference is (12-8) = 4. In the second test case, Alice should eat the candy with sourness 9. Then the maximum difference is (3-1) = 2. In the third test case, Alice should eat the candies with sourness 8, 2, 6, and 7. Then the maximum difference is (10-10) = 0.