Is this an $NP$-complete problem: Product-2-Partition I want to prove the NP-hardness of some problem P in scheduling theory. I was trying with Partition, 3-Partition and Subset product, But neither was successful.

Now, I can reduce a problem, say PRODUCT-2-PARTITION to P, but I am not sure whether such problem is $NP$-complete or not?

The problem PRODUCT-2-PARTITION is as follows:

Given $n$ integers. Can we partition them into $n/2$ subsets, where each subset contains exactly $2$ integers, and the product of the elements of any subset is equal to a given value $B$?
Denote these integers by $x_1\ge x_2\ge\cdots\ge x_n$. We assume these integers are all positive (it is not hard to revise the following algorithm for instances including both positive and negative integers). 

In a valid solution, the greatest element must match the smallest element. Otherwise, say $x_1$ matches $x_i$ where $x_i&gt;x_n$, and $x_n$ matches $x_j$, then $B=x_1x_i&gt;x_1x_n\ge x_jx_n=B$, a contradiction. Hence a valid solution can only be $\{x_1,x_n\},\{x_2,x_{n-1}\},\ldots$ We only need to check whether this partition is valid, i.e. whether $x_1x_n=x_2x_{n-1}=\cdots=B$.