1811C · Restore the Array

Problem: 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 $b_4 = \max(a_4, a_5) = \max(0, 5) = 5$.

You only know the array $b$. Find any matching array $a$ that Kristina may have originally had.

Input Format: 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 $a$.

Output Format: 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.

Note: 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 $a$ = [$0, 0, 3, 4, 3, 3$] :

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