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 Specification

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 Specification

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 seconds per test set.

Memory limit: 1 GB.

Small Dataset

~1 \le T \le 1000~.

~1 \le r,\ t \le 1000~.

Large Dataset

~1 \le T \le 6000~.

~1 \le r \le 10^{18}~.

~1 \le t \le 2 × 10^{18}~.

Sample Input

5
1 9
1 10
3 40
1 1000000000000000000
10000000000000000 1000000000000000000

Sample Output

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