SP327 PLATON - Platon and Socrates

Platon and Socrates one day decided to play a new game. They asked their friend to think of two numbers between $1$ and $5000$, not equal. Then they asked him to tell the product to Platon and the sum to Socrates. After that they tried to figure out what these numbers are. They played a lot of times but none of them could guess these numbers. Finally they made it!! Here is the dialogue: - \[P\] : I don't know the answer. - \[S\] : I knew you wouldn't know, I don't know it either. - \[P\] : Now I know it. - \[S\] : I know it too. Your task is to find all pairs Platon and Socrates could have been thinking about. Numbers are limited to the given range.

Input starts with a single integer $t$, the number of test cases ($t \le 2000$). t test cases follow. Each test case consists of one line containing two integers $l,r$ seperated by a single space, denoting the range of numbers ( $1 \le l < r \le 5000, r-l < 200$ ).

For the $i$-th test case output $a$ line with the text case $i$. In the next line print $n$ - number of pairs from range $(l,r)$. Then exactly $n$ lines follow with two numbers seperated by single space. The first number is not greater than the second. Pairs are printed in increasing sum order.