
    Design a credit assessment algorithm that analyzes an applicant's credit score history to find the most favorable increasing trend in their creditworthiness up to a specific evaluation point, while also considering a projected future credit score. The algorithm should identify the sequence of increasing credit scores that yields the highest cumulative value, starting from any point in their history up to the current evaluation month, and must include their projected credit score for a future month. This assessment helps determine if the applicant's credit history demonstrates a strong positive trajectory when factoring in their expected future financial behavior. The identified sequence must maintain a strictly increasing pattern to reflect consistent credit improvement over time.
    

    
def max_sum_increasing_subseq(a, n, index, k):
    """
    Design a credit assessment algorithm that analyzes an applicant's credit score history to find the most favorable increasing trend in their creditworthiness up to a specific evaluation point, while also considering a projected future credit score. The algorithm should identify the sequence of increasing credit scores that yields the highest cumulative value, starting from any point in their history up to the current evaluation month, and must include their projected credit score for a future month. This assessment helps determine if the applicant's credit history demonstrates a strong positive trajectory when factoring in their expected future financial behavior. The identified sequence must maintain a strictly increasing pattern to reflect consistent credit improvement over time.
    

    """
def max_sum_increasing_subseq(a, n, index, k):
    """
    Design a credit assessment algorithm that analyzes an applicant's credit score history to find the most favorable increasing trend in their creditworthiness up to a specific evaluation point, while also considering a projected future credit score. The algorithm should identify the sequence of increasing credit scores that yields the highest cumulative value, starting from any point in their history up to the current evaluation month, and must include their projected credit score for a future month. This assessment helps determine if the applicant's credit history demonstrates a strong positive trajectory when factoring in their expected future financial behavior. The identified sequence must maintain a strictly increasing pattern to reflect consistent credit improvement over time.
    

    """
    dp = [[0 for i in range(n)] for i in range(n)]
    for i in range(n):
        if a[i] > a[0]:
            dp[0][i] = a[i] + a[0]
        else:
            dp[0][i] = a[i]
    for i in range(1, n):
        for j in range(n):
            if a[j] > a[i] and j > i:
                if dp[i - 1][i] + a[j] > dp[i - 1][j]:
                    dp[i][j] = dp[i - 1][i] + a[j]
                else:
                    dp[i][j] = dp[i - 1][j]
            else:
                dp[i][j] = dp[i - 1][j]
    return dp[index][k]