Factorization

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.

Examples

Input

100000 2

Output

2 50000

Input

100000 20

Output

-1

Input

1024 5

Output

2 64 2 2 2

inputFormat

Input

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

outputFormat

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.

Examples

Input

100000 2

Output

2 50000

Input

100000 20

Output

-1

Input

1024 5

Output

2 64 2 2 2

样例

1024 5

2 2 2 2 64

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