[Solution] Good Arrays CodeChef Solution

Problem

Chef considers an array good if it has no subarray of size less than $N$ such that the GCD of all the elements of the subarray is equal to $1$.

Chef has an array $A$ of size $N$ with him. He wants to convert it into a good array by applying a specific operation.
In one operation, Chef can choose any subarray and reverse it.

Find the minimum number of operations required to convert the array into a good array and the operations themselves. If there are multiple ways to achieve the result, print any.
If it is not possible to convert the array into a good array, print $-1$ instead.

Note: A subarray of an array is formed by deletion of several (possibly zero) elements from the beginning and several (possibly zero) elements from the end of the array.

Input Format

• First line will contain $T$, number of test cases. Then the test cases follow.
• The first line of each test case contains of single integer $N$ denoting the length of the array.
• The second line contains $N$ space-separated integers $A_1, A_2,\ldots, A_N$ representing the initial array.

Output Format

• If there is a way to convert the given array into a good array, then:
  • In a single line, output $X$ denoting the minimum number of operations required.
  • In the following $X$ lines, output $2$ integers - $L$ and $R$ denoting the left and right index of the subarray you want to reverse. Note that, $(1\le L\le R\le N)$.
• If there is no way to convert, print $-1$ in a single line.

Explanation:

Test case $1$: We need only one operation to convert the array into a good array. Choose $L = 2, R = 3$ and reverse the subarray $[2, 6]$ to $[6, 2]$. Thus, the final array is $[3, 6, 2]$. Note that in the final array, no subarray of length less than $N$ has gcd equal to $1$.

Test case $2$: It is not possible to convert the given array to a good array using any number of operations.

Test case $3$: The given array is already good. That is, no subarray of length less than $N$ has gcd equal to $1$. Thus, we need $0$ operations.