CF1909B Make Almost Equal With Mod

[xi - Solar Storm](https://soundcloud.com/yugenero/xi-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 $

Each 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.

For 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.

In 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.