Expected Difference

Given n distinct integer numbers A = { A₁, A₂, …, A_n } and an integer m, then choose m distinct elements B = { B₁, B₂, …, B_m } randomly from A. You are to calculate the expected difference between the largest and smallest number of B.

For example, consider the case where n = 4, m = 2, and A = { 1, 2, 3, 4 }. It has ¹⁄₂ probability to obtain a difference of 1, ¹⁄₃ probability of 2 and ¹⁄₆ probability of 3. So the answer is ¹⁄₂ × 1 + ¹⁄₃ × 2 + ¹⁄₆ × 3, which is equal to ⁵⁄₃ ≈ 1.667.

The input contains multiple test cases.

Each test case contains consists of two lines. The first line gives the integers n (2 ≤ n ≤ 50 000) and m (2 ≤ m ≤ n). The second line gives n distinct integers A₁, A₂, …, A_n. (0 ≤ A_i ≤ 65 536), which will be sorted in increasing order.

A pair of zeroes indicates the end of the input and should not be processed.

Output the answer of each test case on a separate line with the fraction rounded to 3 decimal places.

2 2
1 2
3 2
1 2 3
4 2
1 2 3 4
4 3
2 3 8 9
0 0

1.000
1.333
1.667
6.500