A15412. Array Recovery

For an array of non-negative integers $a$ of size $n$ , we construct another array $d$ as follows: $d_1 = a_1$ , $d_i = |a_i - a_{i - 1}|$ for $2 \le i \le n$ .

Your task is to restore the array $a$ from a given array $d$ , or to report that there are multiple possible arrays.

The first line contains a single integer $t$ ( $1 \le t \le 100$ ) — the number of test cases.

The first line of each test case contains one integer $n$ ( $1 \le n \le 100$ ) — the size of the arrays $a$ and $d$ .

The second line contains $n$ integers $d_1, d_2, \dots, d_n$ ( $0 \le d_i \le 100$ ) — the elements of the array $d$ .

It can be shown that there always exists at least one suitable array $a$ under these constraints.

For each test case, print the elements of the array $a$ , if there is only one possible array $a$ . Otherwise, print $-1$ .

In the second example, there are two suitable arrays: $[2, 8, 5]$ and $[2, 8, 11]$ .