Problem: 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.

Solution (in PYTHON):

Solution:
def splitter():
    N=0
    K=1
    while N<(2*K):
        x=raw_input()
        l=x.split(" ")
        for i in range(2):
            l[i]=int(l[i])
        if l[0]<=10000 and l[0]>=1:
            N=l[0]
        K=l[1]
    return N,K
def lister():
    global N
    l=[]
    while len(l)!=N:
        x=raw_input()
        l=x.split(" ")
        for i in range(N):
            l[i]=int(l[i])
    return l
T=input()
while T>0:
    N,K=splitter()
    l=lister()
    f=[]
    L=[]
    l.sort()
    while len(f)<K:
        f.append(l.pop(0))
    while len(L)<K:
        L.append(l.pop(-1))
    avg=0
    for i in l:
        avg+=i
    avg/=((N-2*K)*1.0)
    avg=str(avg)
    p=0
    l=len(avg)
    for i in range(l):
        if avg[i]==".":
            p=i
    if p==0:
        avg=avg+".000000"
    else:
        if -p-1>6:
            while l-p!=6:
                avg=avg[0,l-p]
        if l-p-1<6:
            for i in range(6-(l-p-1)):
                avg+="0"
    print avg
    T-=1