Find sum of modulo K of first N natural number

Given two integer N ans K, the task is to find sum of modulo K of first N natural numbers i.e 1%K + 2%K + ..... + N%K.

Examples : 

Input : N = 10 and K = 2.
Output : 5
Sum = 1%2 + 2%2 + 3%2 + 4%2 + 5%2 + 6%2 +
 7%2 + 8%2 + 9%2 + 10%2
 = 1 + 0 + 1 + 0 + 1 + 0 + 1 + 0 + 1 + 0
 = 5.

Method 1: 

Iterate a variable i from 1 to N, evaluate and add i%K. 

Below is the implementation of this approach:  

Output : 

5

Time Complexity : O(N).

Auxiliary Space: O(1)

Method 2 : 
Two cases arise in this method.
Case 1: When N < K, for each number i, N >= i >= 1, will give i as result when operate with modulo K. So, the required sum will be the sum of the first N natural number, N*(N+1)/2.
Case 2: When N >= K, then integers from 1 to K in natural number sequence will produce, 1, 2, 3, ....., K - 1, 0 as result when operate with modulo K. Similarly, from K + 1 to 2K, it will produce same result. So, the idea is to count how many numbers of times this sequence appears and multiply it with the sum of first K - 1 natural numbers. 

Below is the implementation of this approach:  

Output : 

5

Time Complexity : O(1).

Auxiliary Space: O(1)