Description

Find $M$ positive integers that sum to $N$ such that their product is as large as possible. Among all optimal solutions, output the lexicographically smallest one.

Input Format

One line containing two positive integers $N, M$.

Output Format

Output $M$ positive integers that sum to $N$ and whose product is as large as possible, separated by spaces. The sequence should be the lexicographically smallest among all optimal solutions.

6 3

2 2 2

Hint

For 100% of the testdata, $1 \le N \le 10^{9}$, $1 \le M \le 10^{6}$. It is guaranteed that $N \ge M$.

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