Given an integer N, the task is to find out 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 return the series which has smallest first term.
Example 1:
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.
Example 2:
Input: N = 6, M = 4
Output: -1
Explanation: It is not possible as the
least GCD sequence will be 1+2+3+4 which
is greater then n, hence print -1.
Your Task:
You dont need to read input or print anything. Complete the function M_sequence() which takes N and M as input parameter and returns th series of M numbers and if there are no series exist returns -1.
Expected Time Complexity: O(sqrt(n))
Expected Auxiliary Space: O(n)
Constraints:
1 <= N <=10^{5}

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