A14674 | Polycarp and Sums of Subsequences

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 $a$ .

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.

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