You are given an integer array nums containing distinct positive integers and an integer target.

Determine if you can partition nums into two non-empty disjoint subsets, with each element belonging to exactly one subset, such that the product of the elements in each subset is equal to target.

Return true if such a partition exists and false otherwise.

A subset of an array is a selection of elements of the array.

 

Example 1:

Input: nums = [3,1,6,8,4], target = 24

Output: true

Explanation: The subsets [3, 8] and [1, 6, 4] each have a product of 24. Hence, the output is true.

Example 2:

Input: nums = [2,5,3,7], target = 15

Output: false

Explanation: There is no way to partition nums into two non-empty disjoint subsets such that both subsets have a product of 15. Hence, the output is false.

 

Constraints: