Infinite Binary Tree

Consider an infinite binary tree built by the following rules. Each node stores an ordered pair of two integers.

1. The root stores (1, 1).
2. If a node stores (a, b), its left child stores (a+b, b), and its right child stores (a, a+b).

Given a node, we want to find a shortest path from the root to that node. The path itself may be very long, so only the number of moves to a left child and the number of moves to a right child are required.

Given two integers A and B, write a program that computes how many times the shortest path from the root to the node storing (A, B) moves to a left child and to a right child.

The first line contains two integers A and B. (1 ≤ A, B ≤ 2,000,000,000)

No invalid input is given.

Print two integers L and R on the first line. L is the number of moves to a left child, and R is the number of moves to a right child.