
    Write a function to analyze sorted historical loan risk scores to determine if a specific risk score threshold represents the majority risk level in the loan portfolio. The function should take as input an array of sorted risk scores from previous loan applications, the total number of applications, and a target risk score threshold. The function must determine if the given risk score threshold appears in more than half of the total loan applications, which would indicate a dominant risk pattern in the portfolio.
    

    
def binary_search(arr, low, high, x):
    if high >= low:
        mid = (low + high) // 2
        if (mid == 0 or x > arr[mid - 1]) and arr[mid] == x:
            return mid
        elif x > arr[mid]:
            return binary_search(arr, mid + 1, high, x)
        else:
            return binary_search(arr, low, mid - 1, x)
    return -1

def is_majority(arr, n, x):
    """
    Write a function to analyze sorted historical loan risk scores to determine if a specific risk score threshold represents the majority risk level in the loan portfolio. The function should take as input an array of sorted risk scores from previous loan applications, the total number of applications, and a target risk score threshold. The function must determine if the given risk score threshold appears in more than half of the total loan applications, which would indicate a dominant risk pattern in the portfolio.
    

    """
def binary_search(arr, low, high, x):
    if high >= low:
        mid = (low + high) // 2
        if (mid == 0 or x > arr[mid - 1]) and arr[mid] == x:
            return mid
        elif x > arr[mid]:
            return binary_search(arr, mid + 1, high, x)
        else:
            return binary_search(arr, low, mid - 1, x)
    return -1

def is_majority(arr, n, x):
    """
    Write a function to analyze sorted historical loan risk scores to determine if a specific risk score threshold represents the majority risk level in the loan portfolio. The function should take as input an array of sorted risk scores from previous loan applications, the total number of applications, and a target risk score threshold. The function must determine if the given risk score threshold appears in more than half of the total loan applications, which would indicate a dominant risk pattern in the portfolio.
    

    """
    i = binary_search(arr, 0, n - 1, x)
    if i == -1:
        return False
    if i + n // 2 <= n - 1 and arr[i + n // 2] == x:
        return True
    else:
        return False