You are given an array a consisting of n element a1, a2, ..., an. For each element ai you must find another element aj (i ≠ j), such that the summation of ai and aj mod (109 + 7) (i.e. (ai + aj) % (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, ..., an (0 ≤ ai < 109 + 7), giving the array a.
For each test case, print a single line containing n space separated elements, such that the ith element is the answer to the ith element in the array a (i.e. the maximum value of (ai + aj) % (109 + 7)).
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.
## Input
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, ..., an (0 ≤ ai < 109 + 7), giving the array a.
## Output
For each test case, print a single line containing n space separated elements, such that the ith element is the answer to the ith element in the array a (i.e. the maximum value of (ai + aj) % (109 + 7)).
[samples]
## Note
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.
**Definitions**
Let $ T \in \mathbb{Z} $ be the number of test cases.
For each test case $ k \in \{1, \dots, T\} $:
- Let $ n_k \in \mathbb{Z} $ denote the size of the array, with $ 2 \leq n_k \leq 10^5 $.
- Let $ A_k = (a_{k,1}, a_{k,2}, \dots, a_{k,n_k}) $ be a sequence of integers where $ 0 \leq a_{k,i} < 10^9 + 7 $.
Let $ M = 10^9 + 7 $.
**Constraints**
1. $ 1 \leq T \leq \text{large} $ (implied by constraints on $ n $)
2. For each $ k \in \{1, \dots, T\} $:
- $ 2 \leq n_k \leq 10^5 $
- $ 0 \leq a_{k,i} < M $ for all $ i \in \{1, \dots, n_k\} $
**Objective**
For each test case $ k $, and for each element $ a_{k,i} $, compute:
$$
b_{k,i} = \max_{\substack{j \in \{1, \dots, n_k\} \\ j \neq i}} \left( (a_{k,i} + a_{k,j}) \bmod M \right)
$$
Output the sequence $ (b_{k,1}, b_{k,2}, \dots, b_{k,n_k}) $.