Yousef has a secret array (a) of (n) strictly positive integers. For each element (a_i), its shadow (b_i) is the sum of all elements in (a) that are strictly smaller than (a_i). Formally: ()b_i = \sum_{\substack{1 \le j \le n\\ a_j \lt a_i}} a_j() You are given the shadow array (b). Your task is to reconstruct the lexicographically smallest valid array (a) consisting of strictly positive integers that satisfies the above condition. If no such array exists, output (-1). The first line 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) ((0 \le b_i \le 2 \cdot 10^{14})) — the shadow array. 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) integers (a_1, a_2, \dots, a_n) ((1 \le a_i \le 10^{18})) — the lexicographically smallest valid array (a) that satisfies the condition. If no valid array exists, output (-1) instead. In the first test case, the answer is (a = 1). Since there is only one element, there are no strictly smaller elements, so its shadow is (0). Thus (a=1) is valid. It is also lexicographically smallest, because the only allowed values are positive integers, and (1) is the smallest possible. In the second test case, the answer is (a = 2,5,2,5,6): For each (2), there is no smaller element in the array, so the shadow is (0). For each (5), the strictly smaller elements are the two (2)'s, so the shadow is (2+2=4). For (6), the strictly smaller elements are two (2)'s and two (5)'s, so the shadow is (2+2+5+5=14). Therefore the shadow array is exactly (b = 0,4,0,4,14). In the third test case, the shadow array fo