780. Reaching Points

A move consists of taking a point (x, y) and transforming it to either (x, x+y) or (x+y, y).

Given a starting point (sx, sy) and a target point (tx, ty), return True if and only if a sequence of moves exists to transform the point (sx, sy) to (tx, ty). Otherwise, return False.

Examples:
Input: sx = 1, sy = 1, tx = 3, ty = 5
Output: True
Explanation:
One series of moves that transforms the starting point to the target is:
(1, 1) -> (1, 2)
(1, 2) -> (3, 2)
(3, 2) -> (3, 5)

Input: sx = 1, sy = 1, tx = 2, ty = 2
Output: False

Input: sx = 1, sy = 1, tx = 1, ty = 1
Output: True

Note:

• sx, sy, tx, ty will all be integers in the range [1, 10^9].

// Modulus Operation
bool reachingPoints(int sx, int sy, int tx, int ty) { // time: O(log(max(tx, ty)))
    while (tx > sx && ty > sy) {
        if (tx > ty) tx %= ty;
        else ty %= tx;
    }
    return (sx == tx && sy <= ty && ((ty - sy) % sx == 0)) 
        || (sy == ty && sx <= tx && ((tx - sx) % sy == 0));
}