Heart Rate

Given a beat count b over p seconds, find the lower and upper bounds on the constant-interval heart rate that could produce it, plus the estimate 60b/p.

Medium4MathImplementationBinary searchBrute forceNo attempts yetTime limit2sMemory limit512 MB

Problem

A common way to check your own heart rate is to put your index and middle finger on your neck next to the windpipe, count the beats you feel over 15 seconds, and multiply that count by four. The beats per minute (BPM) you get this way is only an estimate. In general, if you count bb beats in pp seconds, the BPM is 60b/p60b/p.

In this problem the heart always beats at a constant interval. If tt is the time in seconds between one beat and the next, the Actual Beats Per Minute (ABPM) is defined as 60/t60/t.

A measurement takes a window of exactly pp seconds and counts the beats that fall inside it. Even when the count is bb, more than one value of tt produces that count, so the ABPM is not determined. The ABPM values consistent with counting bb beats in pp seconds form an interval.

Input

The first line contains the number of test cases NN (1N10001 \le N \le 1000).

Each of the next NN lines describes one test case. A line contains the counted number of beats bb (2b10002 \le b \le 1000) and the measuring time pp (0<p<10000 < p < 1000), separated by a space. The value pp is a real number written with 4 digits after the decimal point.

Output

For each test case, print on a single line the lower endpoint of the interval of possible ABPM values, the calculated BPM 60b/p60b/p, and the upper endpoint of that interval, separated by single spaces.

Print all three values rounded to 4 digits after the decimal point, padded with zeros so that exactly 4 digits follow the decimal point.