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?

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 \(a_1,\cdots,a_n(1 \leq a_i \leq 2 * 10^9,\ 1 \leq i \leq n)\).

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