Pilots

At the Byteotian Training Centre, pilots train for missions that demand extraordinary precision and control. One measure of a pilot's skill is how long they can fly a desired route without deviating too much, that is, how steadily they can hold their course.

The task is hard because the simulator is extremely sensitive: it records even the slightest movement of the yoke (the control device used to steer an aircraft). At every moment the simulator stores a single integer describing the yoke's position.

Before each session a tolerance level $t$ is fixed. The pilot must then fly for as long as possible so that every recorded yoke position stays within $t$ of every other. Formally, the flight fragment from moment $i$ to moment $j$ is within tolerance $t$ when the measurements $a_i, a_{i+1}, \dots, a_j$ satisfy $|a_k - a_l| \le t$ for every pair of elements $a_k, a_l$ in it.

Given the tolerance level and the sequence of yoke position measurements, determine the length of the longest flight fragment that stays within the tolerance level $t$.

The first line contains two integers $t$ and $n$ ($0 \le t \le 2\,000\,000\,000$, $1 \le n \le 3\,000\,000$), separated by a single space: the tolerance level and the number of recorded measurements.

The second line contains those $n$ measurements separated by single spaces. Each measurement is an integer between $1$ and $2\,000\,000\,000$.

Print a single integer: the maximum length of a flight fragment that stays within the given tolerance level $t$.