A15777. Restore the Array

Kristina had an array $a$ of length $n$ consisting of non-negative integers.

She built a new array $b$ of length $n-1$ , such that $b_i = \max(a_i, a_{i+1})$ ( $1 \le i \le n-1$ ).

For example, suppose Kristina had an array $a$ = \[ $3, 0, 4, 0, 5$ \] of length $5$ . Then she did the following:

1. Calculated $b_1 = \max(a_1, a_2) = \max(3, 0) = 3$ ;
2. Calculated $b_2 = \max(a_2, a_3) = \max(0, 4) = 4$ ;
3. Calculated $b_3 = \max(a_3, a_4) = \max(4, 0) = 4$ ;
4. Calculated $b_4 = \max(a_4, a_5) = \max(0, 5) = 5$ .

As a result, she got an array $b$ = [ $3, 4, 4, 5$ ] of length $4$ .You only know the array $b$ . Find any matching array $a$ that Kristina may have originally had.

The first line of input data contains a single integer $t$ ( $1 \le t \le 10^4$ ) — the number of test cases.

The description of the test cases follows.

The first line of each test case contains one integer $n$ ( $2 \le n \le 2 \cdot 10^5$ ) — the number of elements in the array $a$ that Kristina originally had.

The second line of each test case contains exactly $n-1$ non-negative integer — elements of array $b$ ( $0 \le b_i \le 10^9$ ).

It is guaranteed that the sum of $n$ over all test cases does not exceed $2 \cdot 10^5$ , and that array $b$ was built correctly from some array $a$ .

For each test case on a separate line, print exactly $n$ non-negative integers — the elements of the array $a$ that Kristina originally had.

If there are several possible answers — output any of them.

The first test case is explained in the problem statement.

In the second test case, we can get array $b$ = \[ $2, 2, 1$ \] from the array $a$ = \[ $2, 2, 1, 1$ \]:

- $b_1 = \max(a_1, a_2) = \max(2, 2) = 2$ ;
- $b_2 = \max(a_2, a_3) = \max(2, 1) = 2$ ;
- $b_3 = \max(a_3, a_4) = \max(1, 1) = 1$ .

In the third test case, all elements of the array $b$ are zeros. Since each $b_i$ is the maximum of two adjacent elements of array $a$ , array $a$ can only consist entirely of zeros.

In the fourth test case, we can get array $b$ = \[ $0, 3, 4, 4, 3$ \] from the array $a$ = \[ $0, 0, 3, 4, 3, 3$ \] :

- $b_1 = \max(a_1, a_2) = \max(0, 0) = 0$ ;
- $b_2 = \max(a_2, a_3) = \max(0, 3) = 3$ ;
- $b_3 = \max(a_3, a_4) = \max(3, 4) = 4$ ;
- $b_4 = \max(a_4, a_5) = \max(4, 3) = 4$ ;
- $b_5 = \max(a_5, a_6) = \max(3, 3) = 3$ .