
    Given a user's historical engagement pattern represented by interaction scores across different content types, find the most significant streak of continuous high engagement that could occur when this behavior pattern repeats k times in future cycles. The engagement pattern consists of n different interaction metrics tracked over time, and your task is to identify the maximum cumulative engagement score possible from any continuous sequence of interactions within the repeated pattern.
    

    
def max_sub_array_sum_repeated(a, n, k):
    """
    Given a user's historical engagement pattern represented by interaction scores across different content types, find the most significant streak of continuous high engagement that could occur when this behavior pattern repeats k times in future cycles. The engagement pattern consists of n different interaction metrics tracked over time, and your task is to identify the maximum cumulative engagement score possible from any continuous sequence of interactions within the repeated pattern.
    

    """
def max_sub_array_sum_repeated(a, n, k):
    """
    Given a user's historical engagement pattern represented by interaction scores across different content types, find the most significant streak of continuous high engagement that could occur when this behavior pattern repeats k times in future cycles. The engagement pattern consists of n different interaction metrics tracked over time, and your task is to identify the maximum cumulative engagement score possible from any continuous sequence of interactions within the repeated pattern.
    

    """
    max_so_far = -2147483648
    max_ending_here = 0
    for i in range(n * k):
        max_ending_here = max_ending_here + a[i % n]
        if max_so_far < max_ending_here:
            max_so_far = max_ending_here
        if max_ending_here < 0:
            max_ending_here = 0
    return max_so_far