> For the complete documentation index, see [llms.txt](https://mayanktyagi3111.gitbook.io/interview-prep/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://mayanktyagi3111.gitbook.io/interview-prep/maths/reaching-points.md).

# 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]`.

```java
class Solution {
    // Similar to GCD
    public boolean helper(int sx, int sy, int tx, int ty) {
        // Cannot go lower than sx
        if (tx < sx)
            return false;
        else if (tx == sx)
            return (ty >= sy && (ty - sy) % tx == 0);
        else
            // Always remove smaller number from bigger number
            return helper(sy, sx, ty % tx, tx);
    }

    public boolean reachingPoints(int sx, int sy, int tx, int ty) {
        if (tx > ty)
            return helper(sy, sx, ty, tx);
        else
            return helper(sx, sy, tx, ty);
    }
}
```