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Series with largest GCD and sum equals to N
Submissions: 454   Accuracy:


  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.

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.

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


24 3
6 4

4 8 12


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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