Description:
The boy Smilo is learning algorithms with a teacher named Brukhovich.
Over the course of the year, Brukhovich will administer $$$n$$$ exams. For each exam, its difficulty $$$a_i$$$ is known, which is a non-negative integer.
Smilo doesn't like when the greatest common divisor of the difficulties of two consecutive exams is equal to $$$1$$$. Therefore, he considers the sadness of the academic year to be the number of such pairs of exams. More formally, the sadness is the number of indices $$$i$$$ ($$$1 \leq i \leq n - 1$$$) such that $$$gcd(a_i, a_{i+1}) = 1$$$, where $$$gcd(x, y)$$$ is the greatest common divisor of integers $$$x$$$ and $$$y$$$.
Brukhovich wants to minimize the sadness of the year of Smilo. To do this, he can set the difficulty of any exam to $$$0$$$. However, Brukhovich doesn't want to make his students' lives too easy. Therefore, he will perform this action no more than $$$k$$$ times.
Help Smilo determine the minimum sadness that Brukhovich can achieve if he performs no more than $$$k$$$ operations.
As a reminder, the greatest common divisor (GCD) of two non-negative integers $$$x$$$ and $$$y$$$ is the maximum integer that is a divisor of both $$$x$$$ and $$$y$$$ and is denoted as $$$gcd(x, y)$$$. In particular, $$$gcd(x, 0) = gcd(0, x) = x$$$ for any non-negative integer $$$x$$$.
Input Format:
The first line contains a single integer $$$t$$$ ($$$1 \leq t \leq 10^4$$$) — the number of test cases. The descriptions of the test cases follow.
The first line of each test case contains two integers $$$n$$$ and $$$k$$$ ($$$1 \leq k \leq n \leq 10^5$$$) — the total number of exams and the maximum number of exams that can be simplified, respectively.
The second line of each test case contains $$$n$$$ integers $$$a_1, a_2, a_3, \ldots, a_n$$$ — the elements of array $$$a$$$, which are the difficulties of the exams ($$$0 \leq a_i \leq 10^9$$$).
It is guaranteed that the sum of $$$n$$$ across all test cases does not exceed $$$10^5$$$.
Output Format:
For each test case, output the minimum possible sadness that can be achieved by performing no more than $$$k$$$ operations.
Note:
In the first test case, a sadness of $$$1$$$ can be achieved. To this, you can simplify the second and fourth exams. After this, there will be only one pair of adjacent exams with a greatest common divisor (GCD) equal to one, which is the first and second exams.
In the second test case, a sadness of $$$0$$$ can be achieved by simplifying the second and fourth exams.