题目描述

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 $1 \mathrm{~cm}$ (one centimetre). A ring of thickness $1 \mathrm{~cm}$ is the space between two concentric circles whose radii differ by $1 \mathrm{~cm}$.

Maria draws the first black ring around a white circle of radius $r \mathrm{~cm}$. 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 $1 \mathrm{~cm}$ around the last black ring.
2. Then she draws a new black ring of thickness $1 \mathrm{~cm}$ around that white ring.

Note that each "white ring" is simply the space between two black rings.

The area of a disk with radius $1 \mathrm{~cm}$ is $\pi \mathrm{cm}^{2}$. One millilitre of paint is required to cover area $\pi \mathrm{cm}^{2}$. 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.

输入格式

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 $t$.

输出格式

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.

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

提示

Limits

Small dataset (11 Pts, Test set 1 - Visible)

• $1 \leq T \leq 1000 .$
• $1 \leq r, t \leq 1000 .$

Large dataset (13 Pts, Test set 2 - Hidden)

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