Leetcode 2919. Minimum Increment Operations to Make Array Beautiful

Make the minimum total +1 increments so every subarray of length ≥3 has max ≥ k — equivalently, choose indices to raise to at least k such that every consecutive triple contains at least one chosen index, minimizing the sum of required increments. This becomes a costed interval-cover/DP optimization: pick positions to cover all length-3 windows at minimum total upgrade cost.