Olympiad

$n$ teams arrived at Programming Competition, each team consists of $a_i(1\le i\le n)$ participants. For competition the classes were prepared with the same number $m$ of computers in each one. Find the minimum number of classes required for competition so that each class will contain participants from different teams only. That is, in any class cannot be more than one participant from one team.

Input

The first line contains the numbers $n$ and $m$. The second line contains $n$ integers $a_i(1\le i\le n)$. All numbers are nonnegative and do not exceed $100$.

Output

Print one number — the minimum required amount of classes.

Examples