The Total is Right

The Total is Right is a popular TV game that has been broadcast in many countries. The goal of the game is to reach a chosen number $N$ using the four arithmetic operations (+, −, ×, ÷) and six given integer numbers $m_i$ for $1 \le i \le 6$. All intermediate numbers must be positive, and any division must be exact (for example, it is not possible to divide 5 by 2). The input numbers $m_i$ as well as all intermediate numbers can be used at most once, but you are not required to use all input numbers.

For instance, suppose $N = 888$ and $m_1 = 100$, $m_2 = 6$, $m_3 = 75$, $m_4 = 3$, $m_5 = 1$, and $m_6 = 6$. We can then obtain $N = 888$ by computing

• 75 − 1 = 74 (using $m_3$/$m_5$)
• 6 + 6 = 12 (using $m_2$/$m_6$)

and finally

• 74 × 12 = 888. (using $m_3$/$m_5$ and $m_2$/$m_6$ respectively)

Hence, in that example, the total is right!

The input file consists of multiple test cases. The first line of the input file consists of a single integer indicating the number of test cases. Each test case follows, and consists of one single line that consists of seven integers $N, m_1, m_2, m_3, m_4, m_5$, and $m_6$, each separated by a single space. The integer $101 \le N \le 999$ is the number that must be reached, and the integers $m_i$ are the numbers that can be used to reach $N$: for each $1 \le i \le 6$, we have $m_i \in \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 25, 50, 75, 100\}$.

For each test case in the input, your program should print one line consisting of the string The total is right (followed by a newline) or of the string Impossible (followed by a newline), depending on whether or not it is possible to obtain exactly $N$ using some or all of the numbers $m_i$ for $1 \le i \le 6$ according to the rules of the game. There should not be any blank lines in your output.