CF571E Geometric Progressions

Geometric progression with the first element $ a $ and common ratio $ b $ is a sequence of numbers $ a,ab,ab^{2},ab^{3},... $ . You are given $ n $ integer geometric progressions. Your task is to find the smallest integer $ x $ , that is the element of all the given progressions, or else state that such integer does not exist.

The first line contains integer ( $ 1

If the intersection of all progressions is empty, then print $ -1 $ , otherwise print the remainder of the minimal positive integer number belonging to all progressions modulo $ 1000000007 $ ( $ 10^{9}+7 $ ).

In the second sample test one of the progressions contains only powers of two, the other one contains only powers of three.