
    Design an algorithm for an automated grading system that calculates how many different ways students can correctly answer n total questions while getting exactly m questions with scores higher than their subsequent questions in the assessment. The system uses this pattern analysis to identify knowledge gaps and provide targeted feedback to students based on their performance across different difficulty transitions.
    

    
def eulerian_num(n, m):
    """
    Design an algorithm for an automated grading system that calculates how many different ways students can correctly answer n total questions while getting exactly m questions with scores higher than their subsequent questions in the assessment. The system uses this pattern analysis to identify knowledge gaps and provide targeted feedback to students based on their performance across different difficulty transitions.
    

    """
def eulerian_num(n, m):
    """
    Design an algorithm for an automated grading system that calculates how many different ways students can correctly answer n total questions while getting exactly m questions with scores higher than their subsequent questions in the assessment. The system uses this pattern analysis to identify knowledge gaps and provide targeted feedback to students based on their performance across different difficulty transitions.
    

    """
    if m >= n or n == 0:
        return 0
    if m == 0:
        return 1
    return (n - m) * eulerian_num(n - 1, m - 1) + (m + 1) * eulerian_num(n - 1, m)