Restore the Array

Description:

Input:

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:

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.

Sample Input:

11
5
3 4 4 5
4
2 2 1
5
0 0 0 0
6
0 3 4 4 3
2
10
4
3 3 3
5
4 2 5 5
4
3 3 3
4
2 1 0
3
4 4
6
8 1 3 5 10

Sample Output:

3 0 4 0 5
2 2 1 1
0 0 0 0 0
0 0 3 4 3 3
10 10
3 3 3 1
4 2 2 5 5
3 3 3 3
2 1 0 0
2 4 4
8 1 1 3 5 10

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

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