hdu5984

  

Pocky

Time Limit: 2000/1000 MS(Java/Others)    Memory Limit: 65536/65536 K (Java/Others)
Total Submission(s): 247    Accepted Submission(s): 119

Problem Description

Let’s talkingabout something of eating a pocky. Here is a Decorer Pocky, with colorfuldecorative stripes in the coating, of length L.
While the length of remaining pocky is longer than d, we perform the followingprocedure. We break the pocky at any point on it in an equal possibility andthis will divide the remaining pocky into two parts. Take the left part and eatit. When it is not longer than d, we do not repeat this procedure.
Now we want to know the expected number of times we should repeat the procedureabove. Round it to 6 decimal places behind the decimal point.

 

 

Input

The first line ofinput contains an integer N which is the number of test cases. Each of the Nlines contains two float-numbers L and d respectively with at most 5 decimalplaces behind the decimal point where 1 ≤ d, L ≤ 150.

 

 

Output

For each testcase, output the expected number of times rounded to 6 decimal places behindthe decimal point in a line.

 

 

Sample Input

6

1.0 1.0

2.0 1.0

4.0 1.0

8.0 1.0

16.0 1.0

7.00 3.00

 

 

Sample Output

0.000000

1.693147

2.386294

3.079442

3.772589

1.847298

 

 

Source

2016ACM/ICPC亚洲区青岛站-重现赛（感谢中国石油大学）

 

 

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