Yousef has a hidden array (a) of length (n) consisting entirely of strictly positive integers. An operation was performed exactly once to create an array (b): Set (b_1 = a_1). For every (i) from (2) to (n), set (b_i = a_i - a_{i-1}). After this, the elements of (b) were completely shuffled. You are given the shuffled array (b). Reconstruct the lexicographically smallest original array (a). If it's impossible for any arrangement of (b) to produce an array (a) of strictly positive integers, output (-1). The first line of input contains an integer (t) ((1 \le t \le 10^4)) — the number of test cases. The first line of each test case contains an integer (n) ((1 \le n \le 2 \cdot 10^5)) — the size of the array. The second line of each test case contains (n) integers (b_1, b_2, \dots, b_n) ((-10^9 \le b_i \le 10^9)) — the elements of the shuffled array (b). It is guaranteed that the sum of (n) over all test cases does not exceed (2 \cdot 10^5). For each test case, output (n) strictly positive integers (a_1, a_2, \dots, a_n) ((a_i \ge 1)) — the lexicographically smallest original array (a). If it's impossible to create a valid array (a), output (-1) instead. In the first test case, the only valid array is (a = 5). In the second test case, there is no valid arrangement of the elements of (b) that reconstructs an array (a) consisting entirely of strictly positive integers. Therefore, the answer is (-1). In the third test case, one valid arrangement reconstructs the array (a=1,1,3,2,6,3). The resulting sequence of differences (1, 0, 2, -1, 4, -3) is a permutation of the given array (b), and among all valid reconstructions, this array is lexicographically smallest.