First N natural can be divided into two sets with given difference and co-prime sums

Given N and M, task is to find whether numbers 1 to N can be divided into two sets such that the absolute difference between the sum of two sets is M and gcd of the sum of two sets is 1 (i.e. Sum of both sets are co-prime). 
Prerequisite : GCD in CPP | GCD
Examples :
 

Input : N = 5 and M = 7 
Output : YES 
Explanation : as numbers from 1 to 5 can be divided into two sets {1, 2, 3, 5} and {4} such that absolute difference between the sum of both sets is 11 - 4 = 7 which is equal to M and also GCD(11, 4) = 1.
Input : N = 6 and M = 3 
Output : NO 
Explanation : In this case, Numbers from 1 to 6 can be divided into two sets {1, 2, 4, 5} and {3, 6} such that absolute difference between their sum is 12 - 9 = 3. But, since 12 and 9 are not co-prime as GCD(12, 9) = 3, the answer is 'NO'.

Approach : Since we have 1 to N numbers, we know that the sum of all the numbers is N * (N + 1) / 2. Let S1 and S2 be two sets such that, 
1) sum(S1) + sum(S2) = N * (N + 1) / 2 
2) sum(S1) - sum(S2) = M 
Solving these two equations will give us the sum of both the sets. If sum(S1) and sum(S2) are integers and they are co-prime (their GCD is 1), then there exists a way to split the numbers into two sets. Otherwise, there is no way to split these N numbers.
Below is the implementation of the solution described above. 
 

Yes

Time Complexity : O(log(n))
Auxiliary Space: O(1)

Please suggest if someone has a better solution which is more efficient in terms of space and time.