This paper presents L-UC, a universal construction that efficiently implements dynamic objects of large state in a wait-free manner. The step complexity of L-UC is O(n+kw), where n is the number of processes, k is the interval contention (i.e., the maximum number of active processes during the execution interval of an operation), and w is the worst-case time complexity to perform an operation on the sequential implementation of the simulated object. L-UC efficiently implements objects whose size can change dynamically. It improves upon previous universal constructions either by efficiently handling objects whose state is large and can change dynamically, or by achieving better step complexity.