Restore Array P

You are given an array \(c\) of length \(n\). Your task is to restore an array \(p\) such that:

\(p_0 = c_0\) and for every \(i\) from \(1\) to \(n-1\), \(p_i = c_i - \max_{0 \le j < i} c_j\).

For example, if \(n=4\) and \(c = [4,7,8,9]\), then:

• \(p_0 = 4\)
• \(p_1 = 7-4 = 3\)
• \(p_2 = 8-\max(4,7)=8-7 = 1\)
• \(p_3 = 9-\max(4,7,8)=9-8 = 1\)

You should implement a program that reads input from stdin and writes the result to stdout.

inputFormat

The first line of input contains a single integer \(T\) (the number of test cases). The description of the test cases follows.

For each test case:

• The first line contains an integer \(n\) (the number of elements in the array \(c\)).
• The second line contains \(n\) space-separated integers representing the array \(c\).

It is guaranteed that \(n \ge 1\).

outputFormat

For each test case, output a single line containing \(n\) space-separated integers representing the restored array \(p\).

## sample

1
4
4 7 8 9

4 3 1 1

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