Interesting and Standard question

You are given N integers (not necessarily distinct) => A1, A2, A3, ..., AN. There are 2N possible subsets (including the empty subset). The GCD of a subset is defined as the greatest common divisor of all the integers in that subset. You need to find the product of the GCDs of all the 2N possible subsets you can construct from A. Since the answer can be large, you need to output the answer modulo 1000000007. Do you think you can solve this question?

Note: The greatest common divisor of an empty subset is 1.

Why it's giving wrong answer , please anyone can help?