title: Find Sum Modulo K First N Natural Number 1
signature: function find_sum_modulo_k_first_n_natural_number_1(n, k)
test_code: 
  
  -- SOLUTION CODE
  -- ============================================
  PLACEHOLDER_CODE_BODY
  
  -- TESTING CODE 
  -- ============================================
  function isCorrect(actual, expected)
      if type(expected) ~= type(actual) then
          return false
      end
      
      if type(expected) == 'table' then
          for k,v_expected in pairs(expected) do
              
              if actual[k] == nil then
                  return false
              end
              local v_actual = actual[k]
              if not isCorrect(v_actual, v_expected) then
                  return false
              end
              actual[k]=nil
          end
      
          if next(actual) then 
              return false
          end
          return true
      else
          return actual == expected
      end
  end
  
  function validateSolution(actual, expected)
      return isCorrect(actual,expected)
  end
  
  function driver(n, k, expected)
      local exec_result;
      local status, error_msg = pcall(function () 
          exec_result=PLACEHOLDER_FN_NAME(n, k) 
      end)
      if status then
          if validateSolution(exec_result,expected) then
              return "PASSED"
          end
          return "FAILED"
      else
          return string.format("ERROR=%s",string.gsub(error_msg,".*:[%d]+: ",""))
      end
  end
      
  function main()
      result = driver(40, 90, 2600)
      print(string.format("TEST-0...%s",result))
  
      result = driver(46, 64, 2530)
      print(string.format("TEST-1...%s",result))
  
      result = driver(97, 20, 1074)
      print(string.format("TEST-2...%s",result))
  
      result = driver(63, 1, 0)
      print(string.format("TEST-3...%s",result))
  
      result = driver(92, 52, 3166)
      print(string.format("TEST-4...%s",result))
  
      result = driver(60, 35, 1345)
      print(string.format("TEST-5...%s",result))
  
      result = driver(67, 40, 1684)
      print(string.format("TEST-6...%s",result))
  
      result = driver(61, 62, 3751)
      print(string.format("TEST-7...%s",result))
  
      result = driver(74, 61, 2311)
      print(string.format("TEST-8...%s",result))
  
      result = driver(67, 41, 1691)
      print(string.format("TEST-9...%s",result))
  
  end
  
  main()
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;
  }