There is a toy building consisting of $n$ towers. Each tower consists of several cubes standing on each other. The $i$-th tower consists of $h_i$ cubes, so it has height $h_i$.

Let's define operation slice on some height $H$ as following: for each tower $i$, if its height is greater than $H$, then remove some top cubes to make tower's height equal to $H$. Cost of one "slice" equals to the total number of removed cubes from all towers.

Let's name slice as good one if its cost is lower or equal to $k$ ($k \ge n$).

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Calculate the minimum number of good slices you have to do to make all towers have the same height. Of course, it is always possible to make it so.

-----Input-----

The first line contains two integers $n$ and $k$ ($1 \le n \le 2 \cdot 10^5$, $n \le k \le 10^9$) — the number of towers and the restriction on slices, respectively.

The second line contains $n$ space separated integers $h_1, h_2, \dots, h_n$ ($1 \le h_i \le 2 \cdot 10^5$) — the initial heights of towers.

-----Output-----

Print one integer — the minimum number of good slices you have to do to make all towers have the same heigth.

-----Examples-----

Input 5 5 3 1 2 2 4

Output 2

Input 4 5 2 3 4 5

Output 2

-----Note-----

In the first example it's optimal to make $2$ slices. The first slice is on height $2$ (its cost is $3$), and the second one is on height $1$ (its cost is $4$).