Time Limit: 1000 ms Memory Limit: 65536 KiB
Binary trees are a common data structure in computer science. In this problem we will look at an infinite
binary tree where the nodes contain a pair of integers. The tree is constructed like this:
• The root contains the pair (1, 1).
• If a node contains (a, b) then its left child contains (a + b, b) and its right child (a, a + b)
Given the contents (a, b) of some node of the binary tree described above, suppose you are walking from
the root of the tree to the given node along the shortest possible path. Can you find out how often you have
to go to a left child and how often to a right child?
The first line contains the number of scenarios.
Every scenario consists of a single line containing two integers i and j (1 ≤ i, j ≤ 2 · 109 ) that represent
a node (i, j). You can assume that this is a valid node in the binary tree described above.
The output for every scenario begins with a line containing “Scenario #i:”, where i is the number of
the scenario starting at 1. Then print a single line containing two numbers l and r separated by a single
space, where l is how often you have to go left and r is how often you have to go right when traversing the
tree from the root to the node given in the input. Print an empty line after every scenario.
3 42 1 3 4 17 73
Scenario #1: 41 0 Scenario #2: 2 1 Scenario #3: 4 6