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Problems

Summer school

Summer school

Time limit 1 second
Memory limit 128 MiB

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 data

Two integer n (1n1000) and k (1k100).

Output data

Print k integers a[1], a[2], ..., a[k], where a[j] (1a[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

Input example #1
7 4
Output example #1
1 3 1 2

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;

Source 2016 Summer Programming School, Uzhgorod, Day 1, Vasyl Biletskiy Contest