A bug starts at position $0$ on the number line and wants to reach its home located at position x.

The bug can move according to the following rules:

• It can jump forward by a positions (moving to position curr + a).

• It can jump backward by b positions (moving to position curr - b).

• It cannot jump backward twice consecutively.

• It cannot land on any position present in the array forbidden.

• It cannot jump to any negative positions.

Return the minimum number of jumps required for the bug to reach position x. If it is impossible to reach position x, return $-1$.

Constraints:

• $1 \leq$ forbidden.length $\leq 1000$

• $1 \leq$ a, b, forbidden[i] $\leq 2000$

• $0 \leq$ x $\leq 2000$

• All elements in forbidden are distinct.

• Position x is not forbidden.

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.