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F. Make k Equal

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou 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.

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.

Examples

Input

6 5 1 2 2 4 2 3

Output

3

Input

7 5 3 3 2 1 1 1 3

Output

4

Codeforces (c) Copyright 2010-2020 Mike Mirzayanov

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