There is an array (a) consisting of (n) non-negative integers and a magic number (k) ((k\ge 1), (k) is an integer). Serval has constructed another array (b) of length (n), where (b_i = a_i \bmod k) holds(^{\text{∗}}) for all (1\leq i\leq n). Then, he shuffled (b). You are given the two arrays (a) and (b). Find a possible magic number (k). However, there is a small possibility that Serval fooled you, and such an integer does not exist. In this case, output (-1). It can be shown that, under the constraints of the problem, if such an integer (k) exists, then there exists a valid answer no more than (10^9). And you need to guarantee that (k\le 10^9) in your output. (^{\text{∗}})(a_i \bmod k) denotes the remainder from dividing (a_i) by (k). Each test contains multiple test cases. The first line contains the number of test cases (t) ((1 \le t \le 10^4)). The description of the test cases follows. The first line of each test case contains an integer (n) ((1\leq n\leq 10^4)) — the length of the array (a). The second line contains (n) integers (a_1, a_2, \ldots, a_n) ((0\leq a_i\leq 10^6)) — the elements of the array (a). The third line contains (n) integers (b_1, b_2, \ldots, b_n) ((0\leq b_i\leq 10^6)) — the elements of the array (b). It is guaranteed that the sum of (n) over all test cases does not exceed (10^4). For each test case, output a single integer (k) ((1\leq k\leq 10^9)) — the magic number you found. Print (-1) if it is impossible to find such an integer. If there are multiple answers, you may print any of them. In the first test case, if (k\ge 3), then (2=a_3\bmod k) should be in the array (b), which leads to a contradiction. For (k = 1), (a_1\bmod k, a_2\bmod k, a_3\bmod k, a_4 \bmod k = 0,0,0,0), which cannot be shuffled to (b). For (k = 2), $$$[a_1\bmod k, a_