Falsification of results#895
In the city of N., the informatics olympiad consists of two rounds, each scored out of points. All participants are numbered from to .
Immediately after the olympiad, the jury received a troubling directive: participant Vasya (numbered ) must finish in position . That is, exactly A - 1 participants must have a higher total score than Vasya across both rounds. The rankings for each round have already been published and cannot be changed. For each round, the list of participants in the order of their placement (from first place to -th) is a permutation of the numbers from to . The jury's task is to assign integer scores from to in each round so that Vasya ends up in position overall, while maintaining the published round rankings.
No two participants may receive the same score within a single round. Identical total scores in the overall standings, however, are permitted.
Your task is to either assign the scores accordingly or determine that it is impossible.
The first line contains two integers , (1 \leq N \leq 200, 1 \leq A \leq N) — the number of participants and the place Vasya must take. The second line contains the participant numbers in order of their place in the first round (from first to -th). The third line contains the same for the second round. The numbers in the second and third lines are separated by spaces.
If it is impossible to assign scores as required, output a single word **Impossible**. Otherwise, on the first line, output **Possible**. On the second line, output integers between and , representing the scores assigned to participants in the first round, where the -th number is the score for the participant who placed -th. On the third line, output integers for the second round in the same way. Numbers in all lines should be space-separated.
No two participants may receive the same score in the same round. If there are multiple valid assignments, output any.
Example 1