k-Factorization

Time Limit: 2 seconds

Memory Limit: 256 megabytes

Description

Given a positive integer n, find k integers (not necessary distinct) such that all these integers are strictly greater than 1, and their product is equal to n.

Input

The first line contains two integers n and k (2 ≤ n ≤ 100000, 1 ≤ k ≤ 20).

Output

If it's impossible to find the representation of n as a product of k numbers, print -1.

Otherwise, print k integers in any order. Their product must be equal to n. If there are multiple answers, print any of them.

Sample Input

Input
100000 2
Output
2 50000 
Input
100000 20
Output
-1
Input
1024 5
Output
2 64 2 2 2 

Sample Output

None

Hint

None

Source

None

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