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D2. Equalizing by Division (hard version)

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputThe only difference between easy and hard versions is the number of elements in the array.

You are given an array $$$a$$$ consisting of $$$n$$$ integers. In one move you can choose any $$$a_i$$$ and divide it by $$$2$$$ rounding down (in other words, in one move you can set $$$a_i := \lfloor\frac{a_i}{2}\rfloor$$$).

You can perform such an operation any (possibly, zero) number of times with any $$$a_i$$$.

Your task is to calculate the minimum possible number of operations required to obtain at least $$$k$$$ equal numbers in the array.

Don't forget that it is possible to have $$$a_i = 0$$$ after some operations, thus the answer always exists.

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 the array and the number of equal numbers required.

The second line of the input contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ ($$$1 \le a_i \le 2 \cdot 10^5$$$), where $$$a_i$$$ is the $$$i$$$-th element of $$$a$$$.

Output

Print one integer — the minimum possible number of operations required to obtain at least $$$k$$$ equal numbers in the array.

Examples

Input

5 3 1 2 2 4 5

Output

1

Input

5 3 1 2 3 4 5

Output

2

Input

5 3 1 2 3 3 3

Output

0

Codeforces (c) Copyright 2010-2020 Mike Mirzayanov

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