# Internet Problem Solving Contest

## 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 NCS and NE – 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 NCS+NE whitespace-separated positive integers giving the IQs of all the students. The first NCS 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