Interstellar Orders: Acceleration¶

Estimated time limit: 0.5 seconds. Memory limit: 128 MB.

On the target judge, use twice the largest per-case median runtime of the reference program, rounded up to a multiple of \(0.5\) seconds. See the reference environment.

Story¶

An interstellar computing center receives a batch of motion-calculation orders. Each model comes with two integer parameters, and the customer asks for distances in a consistent output format.

Formal Problem Statement¶

For each order, given integers \(a,t\) , calculate

\[ d=\left|\frac{at^2}{2}\right| \]

Here \(a\) is the acceleration parameter and \(t\) is the time parameter. Both may be negative. The answer is defined exactly by this formula and is nonnegative.

Input¶

The first line contains the number of orders \(T\) . Each of the next \(T\) lines contains two integers \(a,t\) .

Output¶

Output \(T\) lines, each containing \(d\) with exactly one digit after the decimal point. For \(T=0\) , the output is empty.

Samples¶

Sample 1¶

Input¶

6
0 0
1 1
-1 1
2 -3
-3 -3
10000 10000

Output¶

0.0
0.5
0.5
9.0
13.5
500000000000.0

Sample 2¶

Input¶

4
-10000 -10000
9999 9999
1 -10000
-10000 0

Output¶

500000000000.0
499850014999.5
50000000.0
0.0

Sample 3¶

Input¶

Output¶

Sample Explanation¶

The first three answers in sample 1 are \(0.0,0.5,0.5\) . When \(a=-3,t=-3\) , the answer is \(d=13.5\) . Its final order gives \(500000000000.0\) . Sample 3 has no orders and hence no output.

Constraints and Guarantees¶

For 100% of the data: \(0\le T\le10^4\) and \(|a|,|t|\le10^4\) .

Score	Additional conditions
100%	None