# 1654. Minimum Jumps to Reach Home

https://leetcode.com/problems/minimum-jumps-to-reach-home

## Description

A certain bug's home is on the x-axis at position `x`. Help them get there from position `0`.

The bug jumps according to the following rules:

* It can jump exactly `a` positions **forward** (to the right).
* It can jump exactly `b` positions **backward** (to the left).
* It cannot jump backward twice in a row.
* It cannot jump to any `forbidden` positions.

The bug may jump forward **beyond** its home, but it **cannot jump** to positions numbered with **negative** integers.

Given an array of integers `forbidden`, where `forbidden[i]` means that the bug cannot jump to the position `forbidden[i]`, and integers `a`, `b`, and `x`, return _the minimum number of jumps needed for the bug to reach its home_. If there is no possible sequence of jumps that lands the bug on position `x`, return `-1.`

**Example 1:**

```
**Input:** forbidden = [14,4,18,1,15], a = 3, b = 15, x = 9
**Output:** 3
**Explanation:** 3 jumps forward (0 -> 3 -> 6 -> 9) will get the bug home.
```

**Example 2:**

```
**Input:** forbidden = [8,3,16,6,12,20], a = 15, b = 13, x = 11
**Output:** -1
```

**Example 3:**

```
**Input:** forbidden = [1,6,2,14,5,17,4], a = 16, b = 9, x = 7
**Output:** 2
**Explanation:** One jump forward (0 -> 16) then one jump backward (16 -> 7) will get the bug home.
```

**Constraints:**

* `1 <= forbidden.length <= 1000`
* `1 <= a, b, forbidden[i] <= 2000`
* `0 <= x <= 2000`
* All the elements in `forbidden` are distinct.
* Position `x` is not forbidden.

## ac

```java
```
