Note that this is a harder version of the problem
averageseasy.
One wellknown joke goes as follows: If a bad Computer
Science student drops out of college and goes to a different
college to study Economics instead, he will increase the
average intelligence on both colleges.
In this problem we investigate the math behind this joke.
Given the list of student IQs for both colleges, find the
number of students of Computer Science that can make the joke
true.
Input
The first line of the input file contains an integer
$T$ specifying the number
of test cases. Each test case is preceded by a blank line.
Each test case looks as follows: The first line contains two
positive integers $N_{CS}$
and $N_ E$ – the number of
students of Computer Science and Economics, respectively. The
number of Computer Science students will be at least 2 and
there will be at most $200\,
000$ students in every college.
The following lines contain a total of $N_{CS}+N_ E$ whitespaceseparated
positive integers giving the IQs of all the students. The first
$N_{CS}$ students
mentioned in the input are Computer Science students, the
remaining ones study Economics. The IQ of some students can be
as high as $100\,
000$.
Output
For each test case output a single line with a single
integer – the number of Computer Science students that would
cause the funny event to happen.
Sample Input 1 
Sample Output 1 
1
5 5
100 101 102 103 104
98 100 102 99 101

1
