The Bird tree1 is an infinite binary tree, whose first 5 levels look as follows: This is a co-recursive definition in which both occurrences of bird refer to the full (infinite) tree. The expression bird + 1 means that 1 is added to every fraction in the tree, and 1/bird means that every fraction in the tree is inverted (so a/b becomes b/a). Surprisingly, the tree contains every positive rational number exactly once, so every reduced fraction is at a unique place in the tree. Hence, we can also describe a rational number by giving directions (L for left subtree, R for right subtree) in the Bird tree. For example, 2/5 is represented by LRR. Given a reduced fraction, return a string consisting of L’s and R’s: the directions to locate this fraction from the top of the tree.

On the first line a positive integer: the number of test cases, at most 100. After that per test case:  one line with two integers a and b (1  <= a, b <=  10^9), separated by a ’/’. These represent the numerator and denominator of a reduced fraction. The integers a and b are not both equal to 1, and they satisfy gcd(a, b) = 1. For every test case the length of the string with directions will be at most 10 000.

Per test case:  one line with the string representation of the location of this fraction in the Bird tree.

NWERC2011