Summer school#7801

Summer school

1 second
128 megabytes
Very easy

Once students came to Uzhgorod to the summer algorithmic programming school and formed teams. It is known that each team consists of one, two or three students. Determine how many students were in each team.

Input

Two integers (1 \le n \le 1000) and (1 \le k \le 100).

Output

Print integers a_1, a_2, ..., a_k, where a_j (1 \le a_j \le 3) is the number of students in the -th team. If there is more than one solution, output any. If there is no solution, print "Impossible" (without quotes).

Examples

Example 1

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Note

If students came to the summer school, and there were only teams, then these two configurations are possible:

  • one team of students, one team of students and two teams of student;

  • three teams of students and one team of student;