Robotopia

In Robotopia the robots work together and keep the town running. Each type of robot has a different number of arms and a different number of legs. By day the robots are gathered into groups so that work can be handed out, and by night your job is to count how many robots of each type sit in each group. The robots never hold still, so counting them one by one does not work. After many tries you managed to learn only the total number of legs and the total number of arms in the group.

Every group is made of exactly two different types of robots, and at least one robot of each type is present. You also know how many legs and arms a single robot of each type has. From the observed leg total and arm total, work out how many robots of each type the group holds.

The first line contains the number of test cases $n$ ($1 \le n \le 100$). Each of the next $n$ lines holds one test case as six integers $l_1$ $a_1$ $l_2$ $a_2$ $l_t$ $a_t$ separated by spaces. Here $l_1$ and $a_1$ are the number of legs and arms of one robot of the first type, $l_2$ and $a_2$ are the same for the second type, and $l_t$ and $a_t$ are the observed totals of legs and arms in the group. Every value is between $1$ and $10000$.

For each test case print one line with the two robot counts separated by a space, the count for the first type first. Both counts must be positive integers, so an answer where either count is $0$ is not accepted.

If no answer satisfies the conditions, or if two or more answers do, print a single question mark ? on that line instead.