Subarray Score ≤ K (Sliding-Window)

Given an integer array and an integer K, count the number of contiguous subarrays whose `(sum × length)` score is at most K. Must be O(n). Requirements Given a non-negative integer array arr and integer K, count contiguous subarrays whose score is sum(arr[i..j]) * (j-i+1) <= K in O(n). Clarify that non-negative values are required for the sliding-window monotonicity. Examples arr = [2, 1, 4, 3, 5] K = 5 answer = 5 Each single-element subarray qualifies, while every multi-element subarray has score above 5. Notes Maintain a running sum and left boundary. After adding arr[right], repeatedly remove arr[left] while sum * window_length > K. Once valid, every suffix of the current non-negative window ending at right is also valid, contributing right-left+1 subarrays. Negative values break this monotonicity and require a different problem formulation; do not silently apply the same window. Preparation Implement the window and hand-trace every right endpoint in the example. Test empty input, K=0, zeros, one oversized element, and a window requiring multiple left shifts. State the monotonicity proof and the O(n) amortized argument out loud.