Migrated from Lutece 95 Ants Run!

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Description

Professor Yang likes to play with ants when he is free. What? Are you asking why he plays with ants instead of others? Ah, because ant is the only non-plant living thing which can be found in Qingshuihe Campus of UESTC apart from human beings.

This time, Professor Yang caught several ants after finishing his lecture for freshmen. At the beginning of the game, he puts $N$ ants around a plate and numbers them in clockwise order. The ants are so obedient that they run clockwise under the guide of Professor Yang on the boundary of the plate which is a circle. When one ant catches up with its previous ant, the game is over. Knowing the speed of ants, Professor Yang wants you to help him to adjust the distance between adjacent ants to make the game last longer.

Input

The first line of the input is $T$ (no more than $10000$), which stands for the number of test cases you need to solve.

Each test case begins with N R representing the number of ants participating the game is $N$ and the radius of the circle is $R$ cm. The next line lists $N$ integers and the $i_{th}$ number is the speed (cm/s) of the $i$-th ant in clockwise direction. All numbers are positive integer not larger than $20$.

Output

If the game can last forever, print Inf in a single line, otherwise please output the longest time in seconds each game can last, which should be printed accurately rounded to three decimals.

Samples

2
3 1
1 1 1
3 1
3 2 1

Inf
3.142

Resources

The 8th UESTC Programming Contest Preliminary