Description

Given $n$, you may choose any segment from $a_l$ to $a_r$ ($1\le l\le r\le n$), and add a value $d$ ($-x\le d\le x$) to each element in this segment. Find the maximum length of a strictly increasing subsequence of the array $a$.

Input Format

The first line contains two integers $n, x$.

The second line contains $n$ integers representing $a_1$ to $a_n$.

Output Format

Output one number, the maximum length of a strictly increasing subsequence of the array $a$.

8 10
7 3 5 12 2 7 3 4

5

Hint

For $100\%$ of the testdata, $1\le n\le 2\times 10^5$, $0\leq x\leq10^9$, $1\leq a_i\leq10^9$.

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