Problem H
Voff

Image from wikimedia.org

Then suddenly Atli hears a bark, then another and then over and over. Atli finds the barking quite annoying but he always tries to make the best of a situation so he tries to turn this into a puzzle to solve.

First Atli writes down the current second every time he hears a bark, denoted by a single integer $a_i$. The time of the first bark is then $a_1$ and the time of the last is $a_n$. In Atli’s reality dogs need at least $k$ seconds between barks to breathe.

Thus Atli decides that the puzzle is what the minimum number of dogs that could be barking is. Atli finds this to be a reasonable puzzle. Can you solve it?

Input

The input is two lines. The first line contains two integers $1 \le n,k \le 10^5$. The second line contains $n$ integers $1 \le a_i \le 10^9$.

Output

Print a single integer, the minimum number of dogs that could be barking.

Scoring

3 1
1 2 3

1

3 2
1 2 3

2

3 3
1 2 3

3

3 4
1 2 3

3