Bullseye

Maria paints bullseyes. A bullseye is a group of concentric rings, the black and white pattern used on an archery target.

Maria starts with $t$ millilitres of black paint and draws rings of thickness 1 cm. A ring of thickness 1 cm is the space between two concentric circles whose radii differ by 1 cm.

The first black ring goes around a white circle of radius $r$ cm. After that Maria repeats the following steps for as long as the paint lasts.

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

A white ring is only the gap between two black rings.

A disk of radius 1 cm has area $\pi\ \mathrm{cm}^2$, and one millilitre of paint covers an area of $\pi\ \mathrm{cm}^2$. Find the largest number of black rings Maria can draw.

• Maria draws complete rings only. If the paint that is left is not enough for a whole black ring, she stops at once.
• 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 a space.

Constraints

• $1 \le T \le 6000$
• $1 \le r \le 10^{18}$
• $1 \le t \le 2 \times 10^{18}$

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