Problem Description

Given integers \( N \) and \( K \). Determine if it is possible to construct a sequence \( a \) such that \( a_1 \times a_2 \times \ldots \times a_K = N \). If it is possible, construct one such sequence that is the lexicographically smallest among all possible sequences. Each element of the sequence must be a positive integer greater than or equal to 2.

Input Format

Two positive integers \( N \) and \( K \) are given in one line.

\( N \ K \)

Output Format

If no such sequence exists, output -1. Otherwise, output \( K \) integers.

Sample Input and Output

Sample Input #1

30 3

Sample Output #1

2 3 5

Sample Input #2

30 4

Sample Output #2

-1

Sample Input #3

123456 7

Sample Output #3

2 2 2 2 2 2 1929

Notes/Hints

Constraints

• \( 1 \leq N \leq 10^9 \)
• \( 1 \leq K \leq 10^9 \)

Sample Explanation 1

Since \( 2 \times 3 \times 5 = 30 \), this sequence satisfies the condition. Other sequences like 3 2 5 or 5 2 3 are also possible, but 2 3 5 is the lexicographically smallest.

Sample Explanation 2

It is impossible to construct any sequence under the given conditions.

见题面 Input 部分

见题面 Output 部分