Kangaroo Rock Hopping

You are given n rocks in a row, numbered from 1 to n, with each rock having a certain height. A kangaroo starts at the first rock and wants to reach the last rock by jumping forward. However, the kangaroo is only able to jump from rock i to rock j (with j > i) if the absolute difference in heights does not exceed k.

Formally, the kangaroo can jump from rock i to rock j if:

\(|heights[j] - heights[i]| \leq k\)

Your task is to determine the minimum number of jumps required for the kangaroo to reach the last rock, or print -1 if it is not possible.

Note: The input is provided via stdin and the output should be printed to stdout.

inputFormat

The first line contains two integers n and k separated by a space, where n is the number of rocks and k is the maximum allowed height difference the kangaroo can jump.

The second line contains n integers representing the heights of the rocks from the first to the last.

Constraints:

• 2 ≤ n ≤ 10⁵
• 0 ≤ heights[i] ≤ 10⁹
• 0 ≤ k ≤ 10⁹

outputFormat

Output a single integer representing the minimum number of jumps required for the kangaroo to reach the last rock. If it is not possible to reach the last rock, output -1.

## sample

5 3
1 2 2 5 2

2

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