Written by    23:51 August 16, 2014 


Binary Tree
Time Limit: 1000MS Memory Limit: 65536K
Total Submissions: 6424 Accepted: 2954


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.

Sample Input

Sample Output


这道题首先得明白, (x, y)中如果x>y那么它的父亲则是(x-y, y), 否则是(x, y-x), 这样就得出了下面的代码:

咳咳, 题目到这里显然还没有完, 即使这个题是这么的水, 也不是那么一下两下可以搞定的, 所以只是上面的代码必然超时.

这里超时的原因肯定是当x>y的时候x的值如果只是减一减不够快, 所以这里改成取余就可以了, 这里要注意一下xy中有一个先到一的情况

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