# H :: Largest Disk

Time Limit: 6 Seconds Memory Limit: 262144 KB

In a *l*×*w* rectangle, there are *k* points with integer coordinates. Your job is to find the largest disk such that it can be enter to the rectangle from the east side (the side with length *l*) and then it can be moved toward the west side (in order to exit the rectangle from the west side) while avoiding given points inside the rectangle on its path.

## Input

The first line of the input includes the number of test cases, 1≤*t*≤100. Each test case starts with a line containing three integers, 1≤*l*≤10^{9}, 1≤*w*≤10^{9}, and 1≤*k*≤5000, the number of points. Each of the following *k* lines contains two integers 0<*x*<*w* and 0<*y*<*l*, the coordinates of points.

## Output

For each test case, print one line containing the answer to the question with exactly 2 digits after decimal point.

## Sample Input

3 5 10 0 5 10 2 1 4 4 4 5 10 2 1 7 4 8

## Sample Output

2.50 1.50 1.58Submit

Source: 12th Iran Nationwide Internet Contest I