Problem

You are provided with a function that is supposed to find the maximum sum of a contiguous subarray in a given list of integers. However, the function is broken and needs debugging. After fixing it, extend the functionality to also return the starting and ending indices of that subarray.

Input

• A list of integers nums where -10^4 <= nums[i] <= 10^4.

Output

• An integer representing the maximum sum of the contiguous subarray.
• The starting and ending indices of that subarray in a tuple format (start_index, end_index).

Examples

Example 1:

Input: nums = [-2,1,-3,4,-1,2,1,-5,4]
Output: (6, (3, 6))

Explanation: The contiguous subarray [4,-1,2,1] has the maximum sum of 6.

Example 2:

Input: nums = [1]
Output: (1, (0, 0))

Explanation: The only element is the maximum subarray.

Constraints

• 1 <= nums.length <= 10^5.
• The function should run in O(n) time complexity.