B. Make Almost Equal With Modtime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputxi - Solar Storm⠀You are given an array a_1, a_2, \dots, a_n of distinct positive integers. You have to do the following operation exactly once:  choose a positive integer k;  for each i from 1 to n, replace a_i with a_i \text{ mod } k^\dagger. Find a value of k such that 1 \leq k \leq 10^{18} and the array a_1, a_2, \dots, a_n contains exactly 2 distinct values at the end of the operation. It can be shown that, under the constraints of the problem, at least one such k always exists. If there are multiple solutions, you can print any of them.^\dagger a \text{ mod } b denotes the remainder after dividing a by b. For example:   7 \text{ mod } 3=1 since 7 = 3 \cdot 2 + 1  15 \text{ mod } 4=3 since 15 = 4 \cdot 3 + 3  21 \text{ mod } 1=0 since 21 = 21 \cdot 1 + 0 InputEach test contains multiple test cases. The first line contains the number of test cases t (1 \le t \le 500). The description of the test cases follows.The first line of each test case contains a single integer n (2 \le n \le 100) — the length of the array a.The second line of each test case contains n integers a_1, a_2, \ldots, a_n (1 \le a_i \le 10^{17}) — the initial state of the array. It is guaranteed that all the a_i are distinct.Note that there are no constraints on the sum of n over all test cases.OutputFor each test case, output a single integer: a value of k (1 \leq k \leq 10^{18}) such that the array a_1, a_2, \dots, a_n contains exactly 2 distinct values at the end of the operation.ExampleInput
548 15 22 30560 90 98 120 3086328 769 541 986 215 73451000 2000 7000 11000 1600022 1Output
7
30
3
5000
1000000000000000000NoteIn the first test case, you can choose k = 7. The array becomes [8 \text{ mod } 7, 15 \text{ mod } 7, 22 \text{ mod } 7, 30 \text{ mod } 7] = [1, 1, 1, 2], which contains exactly 2 distinct values (\{1, 2\}).In the second test case, you can choose k = 30. The array becomes [0, 0, 8, 0, 8], which contains exactly 2 distinct values (\{0, 8\}). Note that choosing k = 10 would also be a valid solution.In the last test case, you can choose k = 10^{18}. The array becomes [2, 1], which contains exactly 2 distinct values (\{1, 2\}). Note that choosing k = 10^{18} + 1 would not be valid, because 1 \leq k \leq 10^{18} must be true.
548 15 22 30560 90 98 120 3086328 769 541 986 215 73451000 2000 7000 11000 1600022 1
7 30 3 5000 1000000000000000000
['bitmasks', 'constructive algorithms', 'math', 'number theory', '*1200']