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