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:
- Maria imagines a white ring of thickness 1cm around the last black ring.
- 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
Time limit: 30 6 seconds per test set.
Memory limit: 1GB.
Small dataset (Test set 1 - Visible; 11 Points)
1 ≤ T ≤ 1000.
1 ≤ r, t ≤ 1000.
Large dataset (Test set 2 - Hidden; 13 Points)
1 ≤ T ≤ 6000.
1 ≤ r ≤ 1018.
1 ≤ t ≤ 2 × 1018.
Sample
5 1 9 1 10 3 40 1 1000000000000000000 10000000000000000 1000000000000000000
Case #1: 1 Case #2: 2 Case #3: 3 Case #4: 707106780 Case #5: 49