1. Implement a function to find the maximum sum of a subarray with at most k changes allowed.

2. Write a function to find the minimum length of a subarray with a given sum.

3. Implement a function to find the maximum length of a subarray with the sum of elements divisible by k.

4. Write a function to find the maximum sum of a subarray with at most k negative numbers allowed.

5. Implement a function to find the maximum length of a subarray with the sum of elements equal to a given value and at most k negative numbers allowed.

6. Write a function to find the minimum sum of a subarray with a given length.

7. Implement a function to find the maximum product of a subarray with at most k negative numbers allowed.

8. Write a function to find the longest subarray with the sum of elements divisible by k.

9. Implement a function to find the maximum length of a subarray with the sum of elements equal to a given value and at most k distinct elements.

10. Write a function to find the minimum product of a subarray with a given length.

11. Implement a function to find the maximum length of a subarray with the product of elements equal to a given value and at most k negative numbers allowed.

12. Write a function to find the longest subarray with the product of elements divisible by k.

13. Implement a function to find the maximum length of a subarray with the product of elements equal to a given value and at most k distinct elements.

14. Write a function to find the maximum sum of a subarray with at most k changes allowed and all elements are positive.

15. Implement a function to find the minimum length of a subarray with a given sum and all elements are positive.

16. Write a function to find the maximum length of a subarray with the sum of elements divisible by k and all elements are positive.

17. Implement a function to find the maximum sum of a subarray with at most k changes allowed and all elements are non-negative.

18. Write a function to find the minimum length of a subarray with a given sum and all elements are non-negative.

19. Implement a function to find the maximum length of a subarray with the sum of elements divisible by k and all elements are non-negative.

20. Write a function to find the maximum sum of a subarray with at most k changes allowed and all elements are negative.

21. Implement a function to find the minimum length of a subarray with a given sum and all elements are negative.

22. Write a function to find the maximum length of a subarray with the sum of elements divisible by k and all elements are negative.

23. Implement a function to find the maximum product of a subarray with at most k changes allowed and all elements are positive.

24. Write a function to find the minimum length of a subarray with a given product.

25. Implement a function to find the maximum length of a subarray with the product of elements equal to a given value and at most k changes allowed.

26. Write a function to find the maximum sum of a subarray with at most k changes allowed and all elements are distinct.

27. Implement a function to find the minimum length of a subarray with a given sum and all elements are distinct.

28. Write a function to find the maximum length of a subarray with the sum of elements divisible by k and all elements are distinct.

29. Implement a function to find the maximum product of a subarray with at most k changes allowed and all elements are distinct.

30. Write a function to find the minimum length of a subarray with a given product and all elements are distinct.