title: Count Possible Paths Top Left Bottom Right Nxm Matrix 2
signature: def countPossiblePathsTopLeftBottomRightNxmMatrix2(p: Int, q: Int) = {
test_code: import scala.collection.mutable.HashMap
  import scala.collection.immutable.HashSet
  
  
  // SOLUTION CODE
  // ============================================
  PLACEHOLDER_CODE_BODY
  
  
  // TESTING CODE 
  // ============================================
  def validateSolution(actual: Long , expected: Long): Boolean = {
      actual.toString == expected.toString
  }
  
  def driver(p: Int, q: Int, expected: Long): String = {
      try {
          if (validateSolution(PLACEHOLDER_FN_NAME(p, q),expected)) {
              "PASSED"
          } else{
              "FAILED"
          }
      }catch{
          case e: Exception => {e.getClass.getName}
      }
  
  }
  object QuestionEvaluator extends App {
  
      println(s"TEST-0...${driver(
        70, 5, 
        1088430L    
      )}")   
  
  
      println(s"TEST-1...${driver(
        9, 59, 
        5743572120L    
      )}")   
  
  
      println(s"TEST-2...${driver(
        54, 1, 
        1L    
      )}")   
  
  }
  
source_py: def count_possible_paths_top_left_bottom_right_nxm_matrix_2(p, q):
      dp = [1 for i in range(q)]
      for i in range((p - 1)):
          for j in range(1, q):
              dp[j] += dp[(j - 1)]
      return dp[(q - 1)]
source_cpp: int count_possible_paths_top_left_bottom_right_nxm_matrix_2(int m, int n) {
    int dp [ n ] = {
      1 };
      dp [ 0 ] = 1;
      for ( int i = 0;
      i < m;
      i ++ ) {
        for ( int j = 1;
        j < n;
        j ++ ) {
          dp [ j ] += dp [ j - 1 ];
        }
      }
      return dp [ n - 1 ];
    }