404523: GYM101532 C Large Summation

You are given an array a consisting of n element a₁, a₂, ..., a_n. For each element a_i you must find another element a_j (i ≠ j), such that the summation of a_i and a_j mod (10⁹ + 7) (i.e. (a_i + a_j) % (10⁹ + 7)) is as maximal as possible.

Can you help judges by solving this hard problem?

The first line contains an integer T, where T is the number of test cases.

The first line of each test contains an integer n (2 ≤ n ≤ 10⁵), where n is the size of the array a.

The second line of each test case contains n integers a₁, a₂, ..., a_n (0 ≤ a_i < 10⁹ + 7), giving the array a.

For each test case, print a single line containing n space separated elements, such that the i^th element is the answer to the i^th element in the array a (i.e. the maximum value of (a_i + a_j) % (10⁹ + 7)).

2
3
1 2 3
2
1000000000 1000000000

4 5 5
999999993 999999993

As input/output can reach huge size it is recommended to use fast input/output methods: for example, prefer to use scanf/printf instead of cin/cout in C++, prefer to use BufferedReader/PrintWriter instead of Scanner/System.out in Java.