You are given an integer array nums of length $n$ and an integer k.

An index p (where $0 < p < n - 1$) is considered a peak if nums[p] > nums[p - 1] and nums[p] > nums[p + 1].

A subarray starting at index l and ending at index r (where $0 \leq l \leq r < n$) is considered valid if:

1. It contains exactly $1$ peak index p.

2. The distance from the peak p to each boundary is at most k, meaning $p - l \leq k$ and $r - p \leq k$.

Return the total number of valid subarrays.

Constraints:

• $1 \leq n ==$ nums.length $\leq 10^5$

• $-10^5 \leq$ nums[i] $\leq 10^5$

• $1 \leq$ k $\leq n$

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