Covering with intervals X11795

Given a natural $k$ and several numbers $x_1, \ldots, x_n$, we want to find the smallest possible set of closed intervals of length $k$ that cover those numbers. In other words, we must find a set of intervals $\{[y_1, y_1 + k], \dots, [y_m, y_m + k]\}$ such that

• for every $x_i$, there exists some $j$ such that $x_i \in [y_j, y_j + k]$;

• $m$ is minimum.

For instance, if $k=10$ and the $x_i$’s are $14, 19, 23$ and $27$, a possible solution is $\{[12, 22], [1.8, 2.8]\}$, since every $x_i$ belongs to (at least) one of the two intervals, and it is not possible to cover the four numbers with a single interval.

Input

Input consists of several cases, each of which starts with $k$, followed by $n$, followed by $n$ different numbers. All numbers in the input are integers. Assume $1 \le k, n \le 10^5$.

Output

For every case, print the minimum number of closed intervals of length $k$ that cover the given numbers.