Given an integer range [A,B],

What’s the probability to get a 1-bit if we first randomly choose a number x in the range and then randomly choose a bit from x?
What’s the expected number of bit 1s if we randomly choose a number x in the range?

Input Format

The first line of input is the number of test cases $\mathbf{T}$

Each test cases is a line contains 2 integers $\mbox{A}$ and $\mbox{B}$ separated by a space.

Output Format

For each test case output a line containing 2 float numbers separated by a space. The first one is the probability and the second one is the expected number. You should output the number accurate to 5 fractional digits. 

Constraints

$1\leq T\leq200$

$1\leq A\leq B\leq10^{10}$

Sample Input

1
2 4

Sample Output

0.61111 1.33333

Explanation

(10) (11) (100)

(1) So we got a one in $\frac{1}{3}\times\frac{1}{2}+\frac{1}{3}\times\frac{1}{1}+\frac{1}{3}\times\frac{1}{3}=\frac{11}{18}$

(2) The expected 1 we have is : $1\times\frac{1}{3}+2\times\frac{1}{3}+1\times\frac{1}{3}=\frac{4}{3}$

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