2584 - Split the Array to Make Coprime Products.

Hard

You are given a 0-indexed integer array nums of length n.

A split at an index i where 0 <= i <= n - 2 is called valid if the product of the first i + 1 elements and the product of the remaining elements are coprime.

• For example, if nums = [2, 3, 3], then a split at the index i = 0 is valid because 2 and 9 are coprime, while a split at the index i = 1 is not valid because 6 and 3 are not coprime. A split at the index i = 2 is not valid because i == n - 1.

Return the smallest index i at which the array can be split validly or -1 if there is no such split.

Two values val1 and val2 are coprime if gcd(val1, val2) == 1 where gcd(val1, val2) is the greatest common divisor of val1 and val2.

Example 1:

Input: nums = 4,7,8,15,3,5

Output: 2

Explanation: The table above shows the values of the product of the first i + 1 elements, the remaining elements, and their gcd at each index i. The only valid split is at index 2.

Example 2:

Input: nums = 4,7,15,8,3,5

Output: -1

Explanation: The table above shows the values of the product of the first i + 1 elements, the remaining elements, and their gcd at each index i. There is no valid split.

Constraints:

• n == nums.length

• <code>1 <= n <= 10⁴</code>

• <code>1 <= numsi<= 10⁶</code>