## IPSC 2007

## Problem P – Paradox With Averages

One well-known 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 will investigate the maths behind this joke.

### Problem specification

Given the list of student IQs for each of the two colleges, find the number of
students of Computer Science that can make the joke true – that is,
compute the size of the set { S | S is a student of Computer Science, and
if he went to study Economics, both average IQs would increase }.

### Input specification

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 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.

The following lines contain a total of **N**_{CS}+N_{E} whitespace-separated
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.

### Output specification

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.

### Example

**Input:**

1
5 5
100 101 102 103 104
98 100 102 99 101

**Output:**

1

The average Computer Science IQ increases only if the leaving student is #1 or #2.
Student #1 is too dumb to raise the average IQ for Economics, thus only student #2
remains and the answer is 1.

**Credits:**

**Problemsetter(s):** misof

**Contest-related materials:** misof