Given an integer array nums and an integer k, choose exactly $3$ non overlapping subarrays of nums, each with length k, such that the total sum of their elements is maximized.

Return an array of $3$ integers representing the starting indices of these subarrays. If multiple choices achieve the same maximum total sum, return the one with the smallest lexicographical order.

Note: Subarrays are considered non overlapping if their index ranges do not intersect.

Constraints:

• $1 \leq$ nums.length $\leq 2 \cdot 10^4$

• $1 \leq$ nums[i] $< 2^{16}$

• $1 \leq$ k $\leq \lfloor$ nums.length $/ 3 \rfloor$

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