title: Maximum Sum Subsequence Least K Distant Elements
signature: maximumSumSubsequenceLeastKDistantElements(arr, n, k) {
test_code: import 'dart:convert';
  
  // SOLUTION CODE
  // ============================================
  PLACEHOLDER_CODE_BODY
  
  // TESTING CODE 
  // ============================================
  bool validateSolution(int actual, int expected){
      return actual.toString() == expected.toString();
  }
  
  String driver(arr, n, k, int expected){
      try
      {
          if (validateSolution(PLACEHOLDER_FN_NAME(arr, n, k), expected)){
              return "PASSED";
          }
          return "FAILED";
      }catch(exception_object){
          return exception_object.runtimeType.toString();
      }
  }
  
  int main() {
  
      print("TEST-0...${driver(
          [3, 5, 20, 21, 23, 26, 27, 31, 33, 38, 39, 41, 48, 48, 50, 51, 56, 57, 64, 68, 69, 70, 71, 74, 76, 86, 97], 23, 15, 
          98)
      }");
  
      print("TEST-1...${driver(
          [32, 34, -40, 90, -82, -70, 30, 26, -76, -46, -84, 76, -76], 9, 10, 
          90)
      }");
  
      print("TEST-2...${driver(
          [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 22, 34, 
          0)
      }");
  
      print("TEST-3...${driver(
          [96, 15, 30, 25, 83], 2, 3, 
          96)
      }");
  
      print("TEST-4...${driver(
          [-90, -82, -80, -76, -62, -58, -50, -48, -46, -38, -38, -38, -38, -38, -34, -32, -24, -22, -16, -16, -4, -2, 10, 10, 20, 26, 26, 32, 38, 38, 44, 44, 46, 48, 58, 62, 64, 66, 76, 78, 78, 82, 92, 96, 96, 98], 27, 30, 
          26)
      }");
  
      print("TEST-5...${driver(
          [1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0], 9, 9, 
          1)
      }");
  
      print("TEST-6...${driver(
          [1, 2, 9, 17, 24, 31, 31, 33, 56, 57, 61, 71, 73, 74, 76, 77, 79, 83, 86, 95, 99], 12, 10, 
          72)
      }");
  
      print("TEST-7...${driver(
          [-12, 52, -44, 80, -66, 34, 42, -46, 8, 12, -22, -56, 74, -98, -44, 2, -24, -14, -54, -56, -26, -18, -72], 13, 19, 
          80)
      }");
  
      print("TEST-8...${driver(
          [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 13, 13, 
          1)
      }");
  
      print("TEST-9...${driver(
          [65, 1, 34, 38, 15, 6, 55, 21, 32, 90, 39, 25, 43, 48, 64, 66, 88, 70, 82, 75, 25, 56, 23, 27, 41, 33, 33, 55, 60, 90, 41, 58, 42, 53, 38, 90, 7, 15], 37, 33, 
          155)
      }");
  
      return 0;
  }
source_py: def maximum_sum_subsequence_least_k_distant_elements(arr, N, k):
      MS = [0 for i in range(N)]
      MS[(N - 1)] = arr[(N - 1)]
      for i in range((N - 2), (- 1), (- 1)):
          if (((i + k) + 1) >= N):
              MS[i] = max(arr[i], MS[(i + 1)])
          else:
              MS[i] = max((arr[i] + MS[((i + k) + 1)]), MS[(i + 1)])
      return MS[0]
source_cpp: int maximum_sum_subsequence_least_k_distant_elements(vector<int> arr, int N, int k) {
    int MS [ N ];
    MS [ N - 1 ] = arr [ N - 1 ];
    for ( int i = N - 2;
    i >= 0;
    i -- ) {
      if ( i + k + 1 >= N ) MS [ i ] = max ( arr [ i ], MS [ i + 1 ] );
      else MS [ i ] = max ( arr [ i ] + MS [ i + k + 1 ], MS [ i + 1 ] );
    }
    return MS [ 0 ];
  }