Bullseye
Submit Solution(Code Jam Page)

Problem

Maria has been hired by the Ghastly Chemicals Junkies (GCJ) company to help them manufacture bullseyes. A bullseye consists of a number of concentric rings (rings that are centered at the same point), and it usually represents an archery target. GCJ is interested in manufacturing black-and-white bullseyes.



Maria starts with t millilitres of black paint, which she will use to draw rings of thickness 1cm (one centimetre). A ring of thickness 1cm is the space between two concentric circles whose radii differ by 1cm.

Maria draws the first black ring around a white circle of radius r cm. Then she repeats the following process for as long as she has enough paint to do so:

  1. Maria imagines a white ring of thickness 1cm around the last black ring.
  2. Then she draws a new black ring of thickness 1cm around that white ring.
Note that each "white ring" is simply the space between two black rings.

The area of a disk with radius 1cm is π cm2. One millilitre of paint is required to cover area π cm2. What is the maximum number of black rings that Maria can draw? Please note that:

  • Maria only draws complete rings. If the remaining paint is not enough to draw a complete black ring, she stops painting immediately.
  • There will always be enough paint to draw at least one black ring.

Input

The first line of the input gives the number of test cases, T. T test cases follow. Each test case consists of a line containing two space separated integers: r and t.

Output

For each test case, output one line containing "Case #x: y", where x is the case number (starting from 1) and y is the maximum number of black rings that Maria can draw.

Limits

Small dataset

1 ≤ T ≤ 1000.
1 ≤ r, t ≤ 1000.

Large dataset

1 ≤ T ≤ 6000.
1 ≤ r ≤ 1018.
1 ≤ t ≤ 2 × 1018.

Sample


Input
 
5
1 9
1 10
3 40
1 1000000000000000000
10000000000000000 1000000000000000000



Output
 
Case #1: 1
Case #2: 2
Case #3: 3
Case #4: 707106780
Case #5: 49




Points Correct Attempted
11pt 5843 6182
13pt 1796 4784

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