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We present a scheme to concurrently schedule unicast and multicast traffic in an input-queued switch. It aims at providing high performance under any mix of the two traffic types as well as at avoiding starvation of any connection. The key idea is to schedule the two traffic types independently and in parallel, and then arbitrate among them for access to the switching fabric. The unicast and multicast matchings are combined into a single integrated matching. Edges that are excluded from the integrated matching are guaranteed to receive service at a later time, thus balancing service ratios and preventing starvation. We use simulation to evaluate the performance of a system employing the proposed scheme and show that, despite its simplicity, it achieves the intended goals. We also design an enhanced remainder-service policy to achieve better integration and further improve performance.