You are given an array (a), consisting of (n) positive integers. You are allowed to do the following operation: Select an array (b) of size (n) such that the following properties hold: (0 \leq b_i \leq a_i) for each (1 \leq i \leq n) There exists an index (1\leq i < n) such that (b_1+b_2+\ldots+b_i=b_{i+1}+b_{i+2}+\ldots+b_n). That is, the sum of the prefix of length (i) is equal to the sum of the suffix of length (n-i). (0 \leq b_i \leq a_i) for each (1 \leq i \leq n) There exists an index (1\leq i < n) such that (b_1+b_2+\ldots+b_i=b_{i+1}+b_{i+2}+\ldots+b_n). That is, the sum of the prefix of length (i) is equal to the sum of the suffix of length (n-i). Then, subtract (b_i) from (a_i) for each (1 \leq i \leq n). Your task is to change all the elements to (0). Find the minimum number of operations required. Then, output a way to perform the operations. If it is impossible to change all the elements of (a) to (0) no matter how many operations are used, print (-1) instead. It can be shown that under the constraints of this problem, the smallest number of operations required is at most (17). 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) ((2 \leq n \leq 5\cdot 10^4)) — the length of the array (a). The second line of each test case contains (n) integers (a_1,a_2,\ldots,a_n) ((1 \leq a_i \leq 10^{12})) — denoting the array (a). It is guaranteed that the sum of (n) over all test cases does not exceed (5\cdot 10^4). For each test case, output (-1) if there is no solution. Otherwise, first output an integer (s) ((1 \leq s \leq 17)) – the minimum number of operations to change all the elements of (a) to (0). Then, in the next (s) lines,