Make k Equal
Description
You are given the array $a$ consisting of $n$ elements and the integer $k \le n$.
You want to obtain at least $k$ equal elements in the array $a$. In one move, you can make one of the following two operations:
- Take one of the minimum elements of the array and increase its value by one (more formally, if the minimum value of $a$ is $mn$ then you choose such index $i$ that $a_i = mn$ and set $a_i := a_i + 1$);
- take one of the maximum elements of the array and decrease its value by one (more formally, if the maximum value of $a$ is $mx$ then you choose such index $i$ that $a_i = mx$ and set $a_i := a_i - 1$).
Your task is to calculate the minimum number of moves required to obtain at least $k$ equal elements in the array.
The first line of the input contains two integers $n$ and $k$ ($1 \le k \le n \le 2 \cdot 10^5$) — the number of elements in $a$ and the required number of equal elements.
The second line of the input contains $n$ integers $a_1, a_2, \dots, a_n$ ($1 \le a_i \le 10^9$), where $a_i$ is the $i$-th element of $a$.
Print one integer — the minimum number of moves required to obtain at least $k$ equal elements in the array.
Input
The first line of the input contains two integers $n$ and $k$ ($1 \le k \le n \le 2 \cdot 10^5$) — the number of elements in $a$ and the required number of equal elements.
The second line of the input contains $n$ integers $a_1, a_2, \dots, a_n$ ($1 \le a_i \le 10^9$), where $a_i$ is the $i$-th element of $a$.
Output
Print one integer — the minimum number of moves required to obtain at least $k$ equal elements in the array.
Samples
6 5
1 2 2 4 2 3
3
7 5
3 3 2 1 1 1 3
4