Sergey has made N measurements. Now, he wants to know the average value of the measurements made.
In order to make the average value a better representative of the measurements, before calculating the average, he wants first to remove the highest K and the lowest K measurements. After that, he will calculate the average value among the remaining N - 2K measurements.
Could you help Sergey to find the average value he will get after these manipulations?

Input
The first line of the input contains an integer T denoting the number of test cases. The description of T test cases follows.
The first line of each test case contains two space-separated integers N and K denoting the number of measurements and the number of the greatest and the lowest values that will be removed.
The second line contains N space-separated integers A1, A2, ..., AN denoting the measurements.

Output
For each test case, output a single line containing the average value after removing K lowest and K greatest measurements.
Your answer will be considered correct, in case it has absolute or relative error, not exceeding 10^-6.

Constraints

1 ≤ T ≤ 100
1 ≤ N ≤ 10^4
0 ≤ 2K < N
-10^6 ≤ Ai ≤ 10^6

Example
Input:
3
5 1
2 9 -10 25 1
5 0
2 9 -10 25 1
3 1
1 1 1

Output:
4.000000
5.400000
1.000000

Explanation
Example case 1. After removing 1 greatest and 1 lowest measurement, we get the set {2, 9, 1}. The average value in this set is (2+9+1)/3=4.
Example case 2. The average value in the set {2, 9, -10, 25, 1} is (2+9-10+25+1)/5=5.4.
Example case 3. After removing the 1 largest and smallest measurements, Sergey will be left with only one measurement, i.e. 1. Average of this is 1 itself.

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