Donald is a fence builder. He wants to build a fence that is
$N  1$ meters long. He
needs a fence post every meter along the fence, which means he
needs $N$ fence posts.
Donald has $K$ poles of
varying lengths that he wants to use as fence posts. The fence
posts must have the same lengths, and be as long as possible.
Also, the parts of the poles that are not used for the posts
must not be longer than the ones used for the posts. Donald can
cut the poles as many times as he wants, and at any position he
wants. However, cutting a pole takes time, so he wants to make
as few cuts as possible while achieving his other goals.
How many cuts does Donald have to make to get the fence
posts for his fence?
Input
The first line has two spaceseparated integers,
$K$ and $N$. The second line consists of
$K$ spaceseparated
integers $p_1$,
$p_2$, …, $p_ K$, where $p_ i$ represents the length of the
$i$th pole.
Output
Output the minimum number of cuts needed to build the
fence.
Limits

$1 \leq K \leq N \leq 10\,
000$

$1 \leq p_ i \leq 10\,
000$
Sample Input 1 
Sample Output 1 
1 2
3

1

Sample Input 2 
Sample Output 2 
2 5
4 2

4
