write a go solution for E. Common Generatortime limit per test2 secondsmemory limit per test512 megabytesinputstandard inputoutputstandard outputFor two integers x and y (x,y>=2), we will say that x is a generator of y if and only if x can be transformed to y by performing the following operation some number of times (possibly zero):  Choose a divisor d (d>=2) of x, then increase x by d. For example,   3 is a generator of 8 since we can perform the following operations: 3xarrowd=36xarrowd=28;  4 is a generator of 10 since we can perform the following operations: 4xarrowd=48xarrowd=210;  5 is not a generator of 6 since we cannot transform 5 into 6 with the operation above. Now, Kevin gives you an array a consisting of n pairwise distinct integers (a_i>=2).You have to find an integer x>=2 such that for each 1<=i<=n, x is a generator of a_i, or determine that such an integer does not exist.InputEach test contains multiple test cases. The first line of the input contains a single integer t (1<=t<=10^4) — the number of test cases. The description of test cases follows.The first line of each test case contains a single integer n (1<=n<=10^5) — the length of the array a.The second line contains n integers a_1,a_2,ldots,a_n (2<=a_i<=4*10^5) — the elements in the array a. It is guaranteed that the elements are pairwise distinct.It is guaranteed that the sum of n over all test cases does not exceed 10^5.OutputFor each test case, output a single integer x — the integer you found. Print -1 if there does not exist a valid x.If there are multiple answers, you may output any of them.ExampleInput438 9 1042 3 4 52147 15453 6 8 25 100000Output2
-1
7
3
NoteIn the first test case, for x=2:  2 is a generator of 8, since we can perform the following operations: 2xarrowd=24xarrowd=48;  2 is a generator of 9, since we can perform the following operations: 2xarrowd=24xarrowd=26xarrowd=39.  2 is a generator of 10, since we can perform the following operations: 2xarrowd=24xarrowd=26xarrowd=28xarrowd=210. In the second test case, it can be proven that it is impossible to find a common generator of the four integers.. Output only the code with no comments, explanation, or additional text.