A14055 | Find The Array

You are given an array $[a_1, a_2, \dots, a_n]$ such that $1 \le a_i \le 10^9$ . Let $S$ be the sum of all elements of the array $a$ .

Let's call an array $b$ of $n$ integers beautiful if:

- $1 \le b_i \le 10^9$ for each $i$ from $1$ to $n$ ;
- for every pair of adjacent integers from the array $(b_i, b_{i + 1})$ , either $b_i$ divides $b_{i + 1}$ , or $b_{i + 1}$ divides $b_i$ (or both);
- $2 \sum \limits_{i = 1}^{n} |a_i - b_i| \le S$ .

Your task is to find any beautiful array. It can be shown that at least one beautiful array always exists.

The first line contains one integer $t$ ( $1 \le t \le 1000$ ) — the number of test cases.

Each test case consists of two lines. The first line contains one integer $n$ ( $2 \le n \le 50$ ).

The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ( $1 \le a_i \le 10^9$ ).

For each test case, print the beautiful array $b_1, b_2, \dots, b_n$ ( $1 \le b_i \le 10^9$ ) on a separate line. It can be shown that at least one beautiful array exists under these circumstances. If there are multiple answers, print any of them.