Series with largest GCD and sum equals to N
Submissions: 350   Accuracy:

37.15%

  Difficulty: Medium   Marks: 4

Given an integer N, the task is to print M increasing numbers such that the sum of M numbers is equal to N and the GCD of these M numbers is maximum among all possible combinations (or series) of M numbers.

Note: If two or more such series are possible then print the series which has smallest first term.

Input:
The first line of input contains an integer T denoting the number of test cases. Then T test cases follow.
Each test case contains two integers N and M as input.

Output:
For each test case, In new line print the required series, If no series is possible then print "-1".

Constraints:
1<=T<=100
1<=M6

Example:
Input:
2
24 3
6 4

Output:
4 8 12
-1

Explanation:

Input  : N = 24, M = 3  
Output : 4 8 12  
Explanation : (3, 6, 15) is also a series of M numbers which 
sums to N, but gcd = 3
(4, 8, 12) has gcd = 4 which is the maximum possible.

** For More Input/Output Examples Use 'Expected Output' option **

Contributor: Arun Tyagi
Author: arun03


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