With the increasing popularity of machine-type communication (MTC) devices, several new challenges are encountered by the legacy long term evolution (LTE) system. One critical issue is that a massive number of MTC devices trying to conduct random access procedures may cause significant collisions and long delays. In this work, we present a new random access mechanism by splitting the contention-based preambles in LTE into two logically disjoint parts, one for the user equipment (UE) being paged and the other for the UEs not being paged. Since the IDs of paged UEs are known by the base station, a novel hash-based random access, which we call hint, is possible. The main idea is to pre-allocate preambles to paged UEs in a contention-free manner and confines non-paged UEs to contend in a separate region. We further build a mathematical model to find the optimal ratio of pre-allocated preambles. Extensive simulations are conducted to validate our results.