Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ACM-ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

C. Maximal GCD

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou are given positive integer number *n*. You should create such strictly increasing sequence of *k* positive numbers *a*_{1}, *a*_{2}, ..., *a*_{k}, that their sum is equal to *n* and greatest common divisor is maximal.

Greatest common divisor of sequence is maximum of such numbers that every element of sequence is divisible by them.

If there is no possible sequence then output -1.

Input

The first line consists of two numbers *n* and *k* (1 ≤ *n*, *k* ≤ 10^{10}).

Output

If the answer exists then output *k* numbers — resulting sequence. Otherwise output -1. If there are multiple answers, print any of them.

Examples

Input

6 3

Output

1 2 3

Input

8 2

Output

2 6

Input

5 3

Output

-1

Codeforces (c) Copyright 2010-2017 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Sep/24/2017 04:17:39 (c3).

Desktop version, switch to mobile version.

User lists

Name |
---|