To solve this problem, we can use a loop to iterate through each question and calculate the minimum possible score for each question. We will keep track of the current streak of consecutive correct answers and the current score.

Here is the Python code to solve the problem:

n, m, k = map(int, input().split())

streak = 0
score = 0

for i in range(n):
    if i < m:
        streak += 1
    elif streak >= k:
        streak = 1
        score += 2
    else:
        streak += 1

    score += 1

print(score)

Explanation:

  • We start by initializing the streak and score variables to 0.
  • We use a loop to iterate through each question, represented by the variable i ranging from 0 to n-1.
  • Inside the loop, we check if i is less than m (the number of questions answered correctly). If it is, we increment the streak variable by 1.
  • If i is greater than or equal to m, we check if the current streak is greater than or equal to k. If it is, we have reached the maximum streak and we double the current score by incrementing it by 2. We also reset the streak to 1.
  • Finally, we always increment the score by 1 since each question answered correctly gives us 1 point.
  • After the loop, we print the final score.

This solution has a time complexity of O(n), where n is the total number of questions

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