Difficulty: Hard
Tags: LeetCode, Hard, Math, Number Theory, leetcode-2543, O(log(min(a, b))), O(1)

Problem

There exists an infinitely large grid. You are currently at point (1, 1), and you need to reach the point (targetX, targetY) using a finite number of steps.

In one step, you can move from point (x, y) to any one of the following points:

(x, y - x)
(x - y, y)
(2 * x, y)
(x, 2 * y)

Given two integers targetX and targetY representing the X-coordinate and Y-coordinate of your final position, return true if you can reach the point from (1, 1) using some number of steps, and false otherwise.

Example 1:

Input: targetX = 6, targetY = 9
Output: false
Explanation: It is impossible to reach (6,9) from (1,1) using any sequence of moves, so false is returned.

Example 2:

Input: targetX = 4, targetY = 7
Output: true
Explanation: You can follow the path (1,1) -> (1,2) -> (1,4) -> (1,8) -> (1,7) -> (2,7) -> (4,7).

Constraints:

1 <= targetX, targetY <= 10⁹