title: Find Sum Modulo K First N Natural Number 1
signature: int findSumModuloKFirstNNaturalNumber1(int n, int k) {
test_code: #include <algorithm>
  #include <assert.h>
  #include <cstdlib>
  #include <iostream>
  #include <map>
  #include <set>
  #include <string>
  #include <tuple> 
  #include <unordered_map>
  #include <vector>
  #include <math.h>
  #include <cmath>
  #include <bits/stdc++.h>
  #include <numeric>
  #include <functional>
  
  using namespace std;
  
  // SOLUTION CODE
  // ============================================
  PLACEHOLDER_CODE_BODY
  
  // TESTING CODE 
  // ============================================
  bool validateSolution(int actual, int expected){
      return actual == expected;
  }
  
  string driver(int n, int k, int expected){
      try
      {
          if (validateSolution(PLACEHOLDER_FN_NAME(n, k), expected)){
              return "PASSED";
          }
          return "FAILED";
      }
      catch (const std::overflow_error& exception_obj)
      {
          return typeid(exception_obj).name();
      }
      catch (const std::runtime_error& exception_obj)
      {
          return typeid(exception_obj).name();
      }
      catch (const std::exception& exception_obj)
      {
          return typeid(exception_obj).name();
      }
      catch (...)
      {
          return "UNK_ERROR";
      }
  }
  
  int main() {
      string result = "";
  
      result = driver(40, 90, 2600); 
      cout << "TEST-" << 0 << "..."
           <<  result
           << "\n";
  
      result = driver(46, 64, 2530); 
      cout << "TEST-" << 1 << "..."
           <<  result
           << "\n";
  
      result = driver(97, 20, 1074); 
      cout << "TEST-" << 2 << "..."
           <<  result
           << "\n";
  
      result = driver(63, 1, 0); 
      cout << "TEST-" << 3 << "..."
           <<  result
           << "\n";
  
      result = driver(92, 52, 3166); 
      cout << "TEST-" << 4 << "..."
           <<  result
           << "\n";
  
      result = driver(60, 35, 1345); 
      cout << "TEST-" << 5 << "..."
           <<  result
           << "\n";
  
      result = driver(67, 40, 1684); 
      cout << "TEST-" << 6 << "..."
           <<  result
           << "\n";
  
      result = driver(61, 62, 3751); 
      cout << "TEST-" << 7 << "..."
           <<  result
           << "\n";
  
      result = driver(74, 61, 2311); 
      cout << "TEST-" << 8 << "..."
           <<  result
           << "\n";
  
      result = driver(67, 41, 1691); 
      cout << "TEST-" << 9 << "..."
           <<  result
           << "\n";
  
      return 0;
  }
source_py: def find_sum_modulo_k_first_n_natural_number_1(N, K):
      ans = 0
      y = (N / K)
      x = (N % K)
      ans = ((((K * (K - 1)) / 2) * y) + ((x * (x + 1)) / 2))
      return int(ans)
source_cpp: int find_sum_modulo_k_first_n_natural_number_1(int N, int K) {
    int ans = 0;
    int y = N / K;
    int x = N % K;
    ans = ( K * ( K - 1 ) / 2 ) * y + ( x * ( x + 1 ) ) / 2;
    return ans;
  }