CF2050F Maximum modulo equality

You are given an array $ a $ of length $ n $ and $ q $ queries $ l $ , $ r $ . For each query, find the maximum possible $ m $ , such that all elements $ a_l $ , $ a_{l+1} $ , ..., $ a_r $ are equal modulo $ m $ . In other words, $ a_l \bmod m = a_{l+1} \bmod m = \dots = a_r \bmod m $ , where $ a \bmod b $ — is the remainder of division $ a $ by $ b $ . In particular, when $ m $ can be infinite, print $ 0 $ .

The first line contains a single integer $ t $ ( $ 1 \le t \le 10^4 $ ) — the number of test cases. The first line of each test case contains two integers $ n $ , $ q $ ( $ 1 \le n, q \le 2\cdot 10^5 $ ) — the length of the array and the number of queries. The second line of each test case contains $ n $ integers $ a_i $ ( $ 1 \le a_i \le 10^9 $ ) — the elements of the array. In the following $ q $ lines of each test case, two integers $ l $ , $ r $ are provided ( $ 1 \le l \le r \le n $ ) — the range of the query. It is guaranteed that the sum of $ n $ across all test cases does not exceed $ 2\cdot 10^5 $ , and the sum of $ q $ does not exceed $ 2\cdot 10^5 $ .

For each query, output the maximum value $ m $ described in the statement.

In the first query of the first sample, $ 6 \bmod 3 = 3 \bmod 3 = 0 $ . It can be shown that for greater $ m $ , the required condition will not be fulfilled. In the third query of the first sample, $ 14 \bmod 4 = 2 \bmod 4 = 6 \bmod 4 = 2 $ . It can be shown that for greater $ m $ , the required condition will not be fulfilled.