Problem Description

LL is very lazy. Recently, he is assigned to a dormitory in the 5th floor and sometimes it's hard for him to decide whether to step out for some snack at night. So he choose two positive integers x, y and decide to go or not to go by the low <y mod l> bit of x (l is the length of x in binary representation). If it is "1", he choose to go and if it is "0", he stay in the dormitory.

Input

Each line contain two positive integers a and b (both not larger than 10^7 and a<=b). x is randomly chosen from [a,b]. No limit on y.

Output

For each case, output the probability (accurate to 6 fractional digits) of getting "1".

1 1
3 5

1.000000
0.666667