Klee in Solitary Confinement

Since the traveler came, people in Monstadt have shown great interest in computer programming and algorithms, including Klee, the Spark Knight of the Knights of Favonius.

Source: Genshin Impact Official

Sent to solitary confinement by Jean again, Klee decides to spend her time learning Mo's algorithm, which computes answers to range query problems without modifications in $\mathcal{O}(n^{1.5})$ time.

To check whether Klee has truly mastered the algorithm (or is secretly making more bombs), Jean gives her a problem. You are given an integer sequence $a_1, a_2, \cdots, a_n$ and several queries $[l_i, r_i]$. For each query, find the mode of the contiguous subsequence $a_{l_i}, a_{l_i+1}, \cdots, a_{r_i}$. The mode is the number that appears the most times in the subsequence.

With Mo's algorithm, Klee solves this problem easily, but another problem comes to mind. You are given an integer sequence $a_1, a_2, \cdots, a_n$ of length $n$ and an integer $k$. You may perform the following operation at most once: choose two integers $l$ and $r$ with $1 \le l \le r \le n$, and add $k$ to every $a_i$ with $l \le i \le r$. You may also skip the operation. Choose whether to perform the operation so as to maximize the number of occurrences of the mode of the whole sequence, and output that maximum.

The first line contains two integers $n$ and $k$ ($1 \le n \le 10^6$, $-10^6 \le k \le 10^6$), the length of the sequence and the additive number.

The second line contains $n$ integers $a_1, a_2, \cdots, a_n$ ($-10^6 \le a_i \le 10^6$), the original sequence.

There is only one test case in each test file.

Output one line containing one integer, the maximum number of occurrences of the mode of the whole sequence after performing or skipping the operation.

For the first sample, choose $l = 1$ and $r = 2$. The sequence becomes $\{4, 4, 4, 4, 4\}$. The mode is clearly $4$, which appears $5$ times.

For the second sample, choose $l = 4$ and $r = 6$. The sequence becomes $\{3, 2, 3, 3, 3, 3, 3\}$. The mode is $3$, which appears $6$ times.

For the fourth sample, do not perform the operation. The modes are $1$ and $-2$, which both appear $3$ times.