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.