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Existing Bluetooth-based Private Contact Tracing (PCT) systems can privately detect whether people have come into direct contact with COVID-19 patients. However, we find that the existing systems lack functionality and flexibility, which may hurt the success of the contact tracing. Specifically, they cannot detect indirect contact (e.g., people may be exposed to coronavirus because of used the same elevator even without direct contact); they also cannot flexibly change the rules of "risky contact", such as how many hours of exposure or how close to a COVID-19 patient that is considered as risk exposure, which may be changed with the environmental situation. In this paper, we propose an efficient and secure contact tracing system that enables both direct contact and indirect contact. To address the above problems, we need to utilize users' trajectory data for private contact tracing, which we call trajectory-based PCT. We formalize this problem as Spatiotemporal Private Set Intersection. By analyzing different approaches such as homomorphic encryption that could be extended to solve this problem, we identify that Trusted Execution Environment (TEE) is a proposing method to achieve our requirements. The major challenge is how to design algorithms for spatiotemporal private set intersection under limited secure memory of TEE. To this end, we design a TEE-based system with flexible trajectory data encoding algorithms. Our experiments on real-world data show that the proposed system can process thousands of queries on tens of million records of trajectory data in a few seconds.