LeetCode 3116 (Hard) — binary search + inclusion-exclusion makes it easy

Full walkthrough: https://www.youtube.com/watch?v=vFuFA3ByCs0 LeetCode 3116 — Kth Smallest Amount With Single Denomination Combination. Here’s the trick everyone misses: Brute force (generate all multiples, pick k-th) fails because k can reach 2×10⁹. The real approach: Binary search the answer X Count valid amounts ≤ X using inclusion-exclusion Odd subsets add, even subtract (bitmask over coins) LCM via GCD, break when LCM > X O(n · 2ⁿ · log(k·M)) — passes cleanly. The 26% acceptance rate makes this look harder than it is. Once you see the count(X) monotonic trick, it clicks.