Maximal GCD

题意翻译

请你构造一个长度为 $k$ 的严格上升正整数序列,使得所有数的和恰好为 $n$,并且所有数的最大公约数最大。输出这个序列。如果没有合法的序列输出 $-1$。如果有多个合法的序列,可以输出任意一个。 $1\le n,k\le 10^{10}$

题目描述

You 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.

输入输出格式

输入格式


The first line consists of two numbers $ n $ and $ k $ ( $ 1<=n,k<=10^{10} $ ).

输出格式


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

输入输出样例

输入样例 #1

6 3

输出样例 #1

1 2 3

输入样例 #2

8 2

输出样例 #2

2 6

输入样例 #3

5 3

输出样例 #3

-1