Array Recovery

2000ms

262144K

Description:

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.

Input:

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.

Output:

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

Sample Input:

Sample Output:

1 1 3 8
-1
0 0 0 0 0

Note:

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

Informação

Provedor Codeforces

Código CF1739B