Description

There are $n$ lamps with positions $p_i$, and all $p_i$ are distinct. When the distance between two lamps is less than $dist$, if there is still a lamp that remains on within this safety distance, you may turn off those lamps (that is, if the distance between the $(i-1)$-th and $(i+1)$-th lamps is $\leq dist$, then the $i$-th lamp can be turned off).

While ensuring that the cave remains sufficiently illuminated, find the maximum number of lamps that can be removed within a single contiguous interval.

The lamps nearest to and farthest from the cave entrance must remain on.

Input Format

The first line contains two numbers, $n$ and $dist$.

The second line contains $n$ numbers, the positions $p_i$ of each lamp.

Output Format

Output one number: the maximum number of lamps that can be removed within a single interval.

3 3
1 2 3

1

Hint

For $100\%$ of the testdata, $1 \leq n \leq 10^5$, and $dist$ is guaranteed to be within the range of int.

Translated by ChatGPT 5