Vupsen, Pupsen and 0

题意翻译

### 题目描述 给一个长度为 $n$ 的序列 $a_1,a_2,\dots,a_n$ ，寻找一个长度为 $n$ 序列 $b_1,b_2,\dots,b_n$ ，满足 $\forall i\in\left[1,n\right]b_i\not=0,\ \ \sum\limits_{i=1}^n |b_i|\le10^9,\ \ \sum\limits_{i=1}^n a_i\times b_i=0$ ，可以证明答案一定存在。 ### 输入格式 第一行输入一个正整数 $t$ 表示数据组数。 对于每一组数据，第一行输入一个正整数 $n$ 表示序列长度，第二行 $n$ 个整数表示序列 $a$ 。 ### 输出格式 对于每一组数据，输出一行 $n$ 个整数表示序列 $b$ 。如果有多种答案，输出任意一种。 ### 数据范围 $1\le t\le100,2\le n\le10^5,2\le\sum n\le2\times10^5,-10^4\le a_i\le10^4,a_i\not=0$ 。

题目描述

Vupsen and Pupsen were gifted an integer array. Since Vupsen doesn't like the number $ 0 $ , he threw away all numbers equal to $ 0 $ from the array. As a result, he got an array $ a $ of length $ n $ . Pupsen, on the contrary, likes the number $ 0 $ and he got upset when he saw the array without zeroes. To cheer Pupsen up, Vupsen decided to come up with another array $ b $ of length $ n $ such that $ \sum_{i=1}^{n}a_i \cdot b_i=0 $ . Since Vupsen doesn't like number $ 0 $ , the array $ b $ must not contain numbers equal to $ 0 $ . Also, the numbers in that array must not be huge, so the sum of their absolute values cannot exceed $ 10^9 $ . Please help Vupsen to find any such array $ b $ !

输入输出格式

输入格式

The first line contains a single integer $ t $ ( $ 1 \le t \le 100 $ ) — the number of test cases. The next $ 2 \cdot t $ lines contain the description of test cases. The description of each test case consists of two lines. The first line of each test case contains a single integer $ n $ ( $ 2 \le n \le 10^5 $ ) — the length of the array. The second line contains $ n $ integers $ a_1, a_2, \ldots, a_n $ ( $ -10^4 \le a_i \le 10^4 $ , $ a_i \neq 0 $ ) — the elements of the array $ a $ . It is guaranteed that the sum of $ n $ over all test cases does not exceed $ 2 \cdot 10^5 $ .

输出格式

For each test case print $ n $ integers $ b_1, b_2, \ldots, b_n $ — elements of the array $ b $ ( $ |b_1|+|b_2|+\ldots +|b_n| \le 10^9 $ , $ b_i \neq 0 $ , $ \sum_{i=1}^{n}a_i \cdot b_i=0 $ ). It can be shown that the answer always exists.

输入输出样例

输入样例 #1

3
2
5 5
5
5 -2 10 -9 4
7
1 2 3 4 5 6 7

输出样例 #1

1 -1
-1 5 1 -1 -1
-10 2 2 -3 5 -1 -1

说明

In the first test case, $ 5 \cdot 1 + 5 \cdot (-1)=5-5=0 $ . You could also print $ 3 $ $ -3 $ , for example, since $ 5 \cdot 3 + 5 \cdot (-3)=15-15=0 $ In the second test case, $ 5 \cdot (-1) + (-2) \cdot 5 + 10 \cdot 1 + (-9) \cdot (-1) + 4 \cdot (-1)=-5-10+10+9-4=0 $ .