Mr. Frog’s Problem

Time Limit: 2000/1000 MS (Java/Others)

Memory Limit: 65536/65536 K (Java/Others)

Description

One day, you, a clever boy, feel bored in your math class, and then fall asleep without your control. In your dream, you meet Mr. Frog, an elder man. He has a problem for you.

He gives you two positive integers A and B, and your task is to find all pairs of integers (C, D), such that $A \leq C \leq B,A \leq D \leq B$ and $\frac{A}{B} +\frac{B}{A} \leq \frac{C}{D} + \frac{D}{C}$

Input

first line contains only one integer T ($T\leq 125$), which indicates the number of test cases. Each test case contains two integers A and B ($1 \leq A \leq B \leq 10^{18}$).

Output

For each test case, first output one line "Case #x:", where x is the case number (starting from 1).

Then in a new line, print an integer s indicating the number of pairs you find.

In each of the following s lines, print a pair of integers C and D. pairs should be sorted by C, and then by D in ascending order.

Sample Input

2 10 10 9 27

Sample Output

Case #1: 1 10 10 Case #2: 2 9 27 27 9

Hint

wange2014

Source

2016CCPC东北地区大学生程序设计竞赛 - 重现赛

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