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Problems

Do It Wrong, Get It Right

Do It Wrong, Get It Right

In elementary school, students learn to subtract fractions by first getting a common denominator and then subtracting the numerators. However, sometimes a student will work the problem incorrectly and still arrive at the correct answer. For example, for the problem \includegraphics{https://static.e-olymp.com/content/17/17b9298bff35d33370137855663f36a3c8afde88.jpg} one can subtract the numbers in the numerator and then subtract the numbers in the denominator, simplify and get the answer. i.e. \includegraphics{https://static.e-olymp.com/content/3f/3f140a85857b15a5315e8fa70cfbf45c0da0a384.jpg} For a given fraction \textbf{b/n}, your task is to find all of the values \textbf{a} and \textbf{m}, where \textbf{a} ≥ \textbf{0} and \textbf{m} > \textbf{0}, for which \includegraphics{https://static.e-olymp.com/content/aa/aa8c7ca94856ae7c430974e05ff6c1ed1a4abe5a.jpg} \InputFile Consists of several test cases. Each test case will consist of a single line with two integers \textbf{b }and \textbf{n }(\textbf{1 }≤ \textbf{b}, \textbf{n }≤ \textbf{10^6}). The input will end with a line with two \textbf{0}s. \OutputFile For each case, output all of the requested fractions on a single line, sorted from smallest to largest. For equivalent fractions, print the one with the smaller numerator first. Output each fraction in the form \textbf{a}/\textbf{m} with no spaces immediately before or after the \textbf{/}. Output a single space between fractions. Output no extra spaces, and do not separate answers with blank lines.
Time limit 1 second
Memory limit 64 MiB
Input example #1
9 12
12 14
4 12
0 0
Output example #1
0/24 5/20 8/16 8/8 5/4
0/28 9/21 9/7
0/24 3/18 3/6
Source 2012 Southeast USA Regional Programming Contest, November 10; 2013 Colombian Collegiate Programming League, Contest 1, February 23, Problem C