Summer school

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

Input

Two integer n (1 ≤ n ≤ 1000) and k (1 ≤ k ≤ 100).

Output

Print k integers a[1], a[2], ..., a[k], where a[j] (1 ≤ a[j] ≤ 3) is the number of students in the j-th team. If there is more than one solution, output any. If there is no solution, print "Impossible" (without quotes).

Examples

Note

If 7 students came to the summer school, and there were only 4 teams, then these two configurations are possible:

• one team of 3 students, one team of 2 students and two teams of 1 student;

• three teams of 2 students and one team of 1 student;