The First Maintenance Window

A cloud server is busy during N scheduled maintenance tasks, each represented by a [start, end) time interval. You need to find the earliest time, starting from time 0, where the server is free for a continuous duration of at least K units of time. All inputs are integers. Input Format: The first line contains two integers: N (the number of busy tasks) and K (the required free duration). The next N lines each contain two integers: start and end. Output Format: Print the integer representing the earliest start time of the first available gap of size K. Example: Input: 3 10 15 20 0 2 5 12 Output: 20 Explanation: The busy intervals are [0,2), [5,12), and [15,20). Gaps are [2,5) (size 3), [12,15) (size 3), and [20, infinity). The first gap of at least size 10 starts at 20.