Student Class Allocation

In this problem, you are given $n$ students and $m$ classes, where each class can accommodate at most $c$ students. Each student provides a list of class preferences in order of priority. Your task is to allocate each student to a class according to their preferences. The allocation process is performed in order: for each student, assign them to the first class in their preference list that still has available capacity. If a student cannot be assigned to any of their preferred classes, then the allocation is considered impossible.

Mathematically, if we denote the capacity of each class by $c$, the number of students by $n$, and the number of classes by $m$, then an allocation is valid if for every student $i \ (1 \le i \le n)$, there exists a class $j \ (1 \le j \le m)$ in their preference list such that the total number of students allocated to class $j$ is at most $c$.

If an allocation is possible, output "Possible" followed by the assignment of each student (using 1-indexed class numbers). Otherwise, output "Impossible".

inputFormat

The input is given via standard input (stdin).

The first line contains three space-separated integers: $n$, $m$, and $c$, representing the number of students, the number of classes, and the maximum capacity of each class respectively.

This is followed by $n$ lines. The $i$th line contains a sequence of integers where the first integer $k$ is the number of preferences for the $i$th student, followed by $k$ distinct integers representing the student's class preferences (each integer is between 1 and $m$).

outputFormat

Output the result to standard output (stdout).

If it is possible to allocate all students according to their preferences, print "Possible" on the first line, followed by $n$ lines each containing the allocated class (1-indexed) for the corresponding student.

If it is not possible, output "Impossible".## sample

6 3 2
3 1 2 3
2 2 3
3 1 3 2
1 3
3 2 1 3
2 3 1

Possible
1
2
1
3
2
1