Time Limit:1000ms Memory Limit:65536KB

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 change the order of the ants and
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 (without quotes) 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 tha 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.

Sample Input

2
3 1
1 1 1
3 1
3 2 1

Sample Output

Inf
3.142

Hint


Author

Source

The 8th UESTC Programming Contest Final