Global warming

Global warming is an important issue and Johnny knows about it. He decided to analyze historical temperatures and find a subsequence of days (not necessarily consecutive) where the temperature was strictly increasing. That will convince the non-believers!

Johnny has found historical data from $n$ consecutive days. The temperature on the $i$-th day was $t_i$.

Formally, we are interested in finding the length of the longest increasing subsequence (LIS) of $(t_1, t_2, \ldots, t_n)$, that is, the largest possible $k$ for which it is possible to choose an increasing sequence of indices $1 \le a_1 < a_2 < \ldots < a_k \le n$ such that $t_{a_1} < t_{a_2} < \ldots < t_{a_k}$.

Johnny wants to find a really long subsequence, and that is why he decided to cheat a bit. He will first choose a non-empty interval of days and an integer $d$ ($-x \le d \le x$), and he will increase the temperature on each of those days by $d$. A small change like that probably will not be noticed by the community, while at the same time it should make the LIS longer. It is allowed to choose $d = 0$.

What is the largest possible length of the LIS after a change?

The first line of the standard input contains two space-separated integers $n$ and $x$ ($1 \le n \le 200\ 000$, $0 \le x \le 10^9$), the number of days and the limit for the absolute value of $d$.

The second line contains $n$ integers $t_1, t_2, \ldots, t_n$ ($1 \le t_i \le 10^9$) separated by spaces, the sequence of historical temperatures.

Print one integer, the largest possible length of the LIS after a single change.