Problem F: Fencing Hall

## Problem F: Fencing Hall

Time Limit: 4 Sec  Memory Limit: 128 MB
Submit: 1804  Solved: 478
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## Description

Dateri has a magic sequence and LowbieH is interested in it. Dateri promises that if LowbieH can answer his question, then he will play fencing with LowbieH. We denote the magic sequence by $$\{a_n\}$$ and Dateri will choose a lucky number $$k$$. He asks LowbieH to find length of the longest consecutive subsequence such that the absolute difference between any two number in the subsequence will not exceed $$k$$. Can you help LowbieH?

## Input

The first line contains two integers $$k(0 \leq k \leq 2*10^9)$$ and $$n(1 \leq n \leq 3 * 10^6)$$.

The second line contains $$n$$ integers $$a_1,\cdots,a_n(1 \leq a_i \leq 2 * 10^9,\ 1 \leq i \leq n)$$.

## Output

One line contains the answer, i.e. the length of the longest available consecutive subsequence.

## Sample Input

3 9
5 1 3 5 8 6 6 9 10

## Sample Output

4

## HINT

There are two available consecutive subsequences : $$\{5,8,6,6\}$$ and $$\{8,6,6,9\}$$.

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