Sliding window on subarray sum equals k

This function should count contiguous subarrays whose sum equals k. It passes all tests with positive numbers but returns 2 for nums = [1, -1, 1, -1], k = 0 — the correct answer is 4 ([1,-1], [-1,1], [1,-1] and [1,-1,1,-1]). Explain why and fix it.

1def count_subarrays(nums, k):
2    count = 0
3    left = 0
4    window = 0
5    for right, x in enumerate(nums):
6        window += x
7        while window > k and left <= right:
8            window -= nums[left]
9            left += 1
10        if window == k:
11            count += 1
12    return count

1. State the property of the input that the sliding window relies on and show which line encodes it.
2. Trace [1, -1, 1, -1], k = 0 and show a valid subarray the window skips.
3. Explain why no two-pointer scheme can be correct here, regardless of tweaks.
4. Give the correct O(n) algorithm and its space cost.
5. List edge cases: k = 0, all zeros, the empty prefix.