407713: GYM102881 B Anany in the Army

Anany was happily doing his military service, but someday he got bored. He was daydreaming about the moment he gets back to problem-solving when he suddenly noticed three sticks on the ground. He challenged his soul (pun intended) to solve the following problem:

You can choose $$$\textbf{one}$$$ stick and increase its length by any amount (integer or non-integer) less than or equal to $$$k$$$ units. You will then form a triangle using the sticks. What is the maximum area of a triangle that you can get?

The first line of input contains an integer $$$T$$$, the number of test cases.

Each of the next $$$T$$$ lines contains 4 space-separated integers each — the lengths of the 3 sticks, followed by $$$k$$$.

All the numbers are positive integers and do not exceed $$$10^4$$$.

It's guaranteed you can always form a non-degenerate triangle.

For each test case, print the maximum area on a single line. The answer will be considered correct if its absolute or relative error does not exceed $$$10^{-4}$$$.

2
1 1 1 2
3 4 4 1

0.500000000
6.928203230