Bullseye

Maria works for a company that manufactures black-and-white bullseyes. A bullseye is a stack of rings formed between concentric circles, circles that share one center, and it usually represents an archery target.

Maria has $t$ millilitres of black paint, and she draws rings of thickness 1cm with it. 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. After that she repeats the following process for as long as she has enough paint.

1. Maria imagines a white ring of thickness 1cm around the last black ring.
2. She draws a new black ring of thickness 1cm around that white ring.

Each white ring is only the empty space left between two black rings.

A disk of radius 1cm has area $\pi$ cm$^2$. One millilitre of paint covers area $\pi$ cm$^2$. Find the maximum number of black rings Maria can draw. Note these two conditions.

• Maria draws complete rings only. If the paint left is not enough for one whole black ring, she stops immediately.
• The paint is always enough for at least one black ring.

The first line contains the number of test cases $T$. Each of the next $T$ lines contains two integers $r$ and $t$ separated by one space.

Constraints

• $1 \le T \le 1000$
• $1 \le r \le 10^{18}$
• $1 \le t \le 10^{18}$
• $2r + 1 \le t$, so at least one black ring always fits.

For each test case, print one line in the form Case #x: y, where $x$ is the test case number starting from 1 and $y$ is the maximum number of black rings Maria can draw.