Polycarp and Sums of Subsequences

题意翻译

Polycarp 的数组 $a$ 包含 $3$ 个正整数。他写出了这个数组中每个非空子集中元素的和，并将它们按单调不下降排序，得到了一个由 $7$ 个整数组成的数组 $b$。 例如，如果 $a=\{1,4,3\}$ ，Polycarp 就会写出$1,4,3,1+4= 5,1+3= 4,4+3= 7,1+4+3=8$。排序之后，他得到一个数组$b=\{1,3,4,4,5,7,8\}$。 不幸的是，Polycarp丢失了数组 $a$ 。他只剩下 $b$ 数组了。请帮助他恢复阵列 $a$ 。

题目描述

Polycarp had an array $ a $ of $ 3 $ positive integers. He wrote out the sums of all non-empty subsequences of this array, sorted them in non-decreasing order, and got an array $ b $ of $ 7 $ integers. For example, if $ a = \{1, 4, 3\} $ , then Polycarp wrote out $ 1 $ , $ 4 $ , $ 3 $ , $ 1 + 4 = 5 $ , $ 1 + 3 = 4 $ , $ 4 + 3 = 7 $ , $ 1 + 4 + 3 = 8 $ . After sorting, he got an array $ b = \{1, 3, 4, 4, 5, 7, 8\}. $ Unfortunately, Polycarp lost the array $ a $ . He only has the array $ b $ left. Help him to restore the array $ a $ .

输入输出格式

输入格式

The first line contains one integer $ t $ ( $ 1 \le t \le 5000 $ ) — the number of test cases. Each test case consists of one line which contains $ 7 $ integers $ b_1, b_2, \dots, b_7 $ ( $ 1 \le b_i \le 10^9 $ ; $ b_i \le b_{i+1} $ ). Additional constraint on the input: there exists at least one array $ a $ which yields this array $ b $ as described in the statement.

输出格式

For each test case, print $ 3 $ integers — $ a_1 $ , $ a_2 $ and $ a_3 $ . If there can be several answers, print any of them.

输入输出样例

输入样例 #1

5
1 3 4 4 5 7 8
1 2 3 4 5 6 7
300000000 300000000 300000000 600000000 600000000 600000000 900000000
1 1 2 999999998 999999999 999999999 1000000000
1 2 2 3 3 4 5

输出样例 #1

1 4 3
4 1 2
300000000 300000000 300000000
999999998 1 1
1 2 2

说明

The subsequence of the array $ a $ is a sequence that can be obtained from $ a $ by removing zero or more of its elements. Two subsequences are considered different if index sets of elements included in them are different. That is, the values of the elements don't matter in the comparison of subsequences. In particular, any array of length $ 3 $ has exactly $ 7 $ different non-empty subsequences.