Given an array of integers nums (which may include negative numbers) and an integer k, find the length of the longest contiguous subarray whose elements sum to exactly k. Return 0 if no such subarray exists. Checking every window works, but re-summing from scratch for every (start, end) pair wastes the fact that a running total only changes by one element at a time. The prefix sumPrefix SumThe running total of all elements from the start of the array up to a given index — precomputing it lets you get the sum of any range in O(1) by subtracting two prefix sums. technique turns this into a single pass: if two prefixes differ by exactly k, the subarray between them sums to k — and a hash map that remembers the first index each prefix sum was seen at finds the longest such subarray in O(n).