Monotonic queue optimizes DP with window constraints. But some DPs have a different constraint: "use exactly k elements". Aliens Trick (WQS Binary Search) handles this.
Instead of fixing k, we add a penalty λ per element and binary search on λ. The idea: with the right penalty, the unconstrained optimum naturally uses exactly k elements. This is a effective meta-technique. It transforms constrained problems into simpler unconstrained ones.