For the Lunar New Year festival this year, James was put in charge of coordinating the dragon dancers. He organized his team of $$$n$$$ dancers in a line such that position 1 is the front of the line. While he trained them all well, he forgot to consider one factor: their heights. When controlling the dragon puppet, it looks quite unnatural if two consecutive people in the line have their heights differ by too much. Additionally, they have been training in their current line order for so long that no dancer can dance directly behind a new person; they must either dance behind the same person or be the front of the line. James wants to pick some dancers from this line to perform in the dance tonight. Help him figure out the length of the longest possible line he can form for tonight's dragon dance!
The first line of input contains two integers $$$n$$$ ($$$1\leq n \leq 2\cdot10^5$$$) and $$$k$$$ ($$$1\leq k \leq 10^9$$$) — the number of dancers and the maximum absolute height difference allowed.
The second line contains $$$n$$$ integers $$$h_1,h_2,\dots,h_n$$$ ($$$1\leq h_i\leq 10^9$$$) — the heights of each of the dancers in the line in order.
The output should consist of a single integer indicating the length of the longest possible line James can form to ensure the dragon dance looks natural.
7 41 2 1 2 6 7 1
6
6 37 4 7 4 8 9
4
In the first sample, James picks the first 6 dancers since the gap between 7 and 1 is too large to be included in the line.
