The Quest Begins (The "Why") I still remember the first time I stared at a competitive‑programming statement and felt my brain short‑circuit. The problem talked about “arrays of length n where each element is at most 10⁹ and you need to count pairs whose sum is divisible by k”. I started scribbling brute‑force loops, then switched to sorting, then tried hash maps… and after twenty minutes I was still staring at a blank editor, wondering if I’d missed some hidden trick. Sound familiar? Y...