RoAlgo Contest #8 | SuperLiga

Task

A ranking line of the form $(M, V, E, I, P)$ — (matches, victories, draws, defeats, points) is given, where some of the values may be denoted with a question mark ($?$) but not $M$. This ranking line corresponds to the results of a team throughout a competitive season in a football league in Southeast Europe.

Now B.B.C, a specialist in the field, wants to know if we can obtain a configuration starting from the current configuration that is valid according to football rules ($3$ points for a victory, $1$ point for a draw, $0$ points for defeats), or if it is impossible. This can be done by replacing the question marks with natural numbers.

For example, the configuration $(5, ?, 1, ?, 10)$ is valid because we can obtain the configuration $(5, 3, 1, 1, 10)$ — $3$ victories, $1$ draw, and $1$ defeat.

Note that the number of matches is always known.

Input data

The first line will contain the number of tests $T$.

Each of the next $T$ lines will contain a configuration in the format described in the statement, each of the $5$ positions can contain either the character ? or a natural number, representing the corresponding number for that position.

Output data

Each line will contain either a valid configuration starting from the given input configuration or the message Impossible if it is not possible.

Any valid configuration is accepted.

Constraints and clarifications

• $1 \leq T \leq 10^5$
• $0 \leq M, V, E, I, P \leq 10^7$

Example

stdin

17
5 ? ? ? ?
9 4 ? 4 ?
7 ? ? 5 4
4 1 2 1 6
6 3 ? 4 12
9 ? 4 ? 13
14 5 ? ? 13
58 28 ? ? 94
100 ? ? 43 120
10 ? ? ? ?
10 4 3 3 ?
10 4 3 ? ?
10 4 ? 3 ?
10 4 ? ? ?
10 ? 3 3 ?
10 ? 3 ? ?
10 ? ? 3 ?

stdout

5 0 0 5 0
9 4 1 4 13
7 1 1 5 4
Impossible
Impossible
9 3 4 2 13
Impossible
58 28 10 20 94
Impossible
10 0 0 10 0
10 4 3 3 15
10 4 3 3 15
10 4 3 3 15
10 4 0 6 12
10 4 3 3 15
10 0 3 7 3
10 0 7 3 7