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A. k-Factorization

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputGiven 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

Codeforces (c) Copyright 2010-2017 Mike Mirzayanov

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