Problem Statement

There are $N$ pins standing on a number line. The coordinate of the $i$-th pin from the left is $X_i$.

You came up with the following game.

You choose some of the pins and remove them so that the distances between the remaining pins are all at least $K$.

Find the maximum number of pins that can remain.

Input

$N\ K$
$X_1\ X_2\ \cdots\ X_N$

• $1 \le N \le 3\times 10^5$
• $1 \le K \le 10^9$
• $-10^9 \le X_1 \lt X_2 \lt \cdots \lt X_N \le 10^9$
• All inputs are integers.

Output

Print the answer on $1$ line, followed by a newline.

Sample

5 3
1 2 5 6 8

3

5 2
1 2 3 4 5

3