Moogle

You got the original idea of making map software, called Moogle Maps,
for the new cool Mapple mPhone.  It will even be capable of indicating
the location of a house address like "13 Main Street".  However, since
the mPhone has limited storage capacity, you need to reduce the data
amount.  You do not want to store the exact location of every single
house number.  Instead only a subset of the house numbers will be
stored exactly, and the others will be linearly interpolated.  So you
want to select house numbers that will minimise the largest
interpolation error, given how many house locations you have capacity
to store.  We view the street as a straight line, and you will always
store the first and the last house location.

Given that you've stored the locations x_i and x_j for the houses with
numbers i and j respectively, but no other house in between, the
interpolated value for a house with number k with i < k < j is 
x_i + (x_j - x_i)(k - i) / (j - i).

Input 

The first line of input gives a single integer, 1 <= t <= 50 , the
number of test cases. 

For each test case, there are two lines. The first contains h and c
(with 2 <= h <= 100 and 2 <= c <= h), where h is the number of houses
on the street and c is the number of house locations that can be
stored.  Houses are numbered consecutively 1, 2, 3, ..., h in the
of their locations on the street.  The second input line contains h
integers in increasing order giving the location of the h houses.  Each
location is in the interval [0, 1000000].

Output 

For each test case, output the maximum interpolation error over all h
houses for the optimal selection of c house locations to store.  The
output should be given with 1 decimal place.

Sample Input

2 
4 2
0 10 19 40
4 3
0 9 20 40

Sample Output  

7.7
1