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This paper targets to a novel but practical recommendation problem named exact-K recommendation. It is different from traditional top-K recommendation, as it focuses more on (constrained) combinatorial optimization which will optimize to recommend a whole set of K items called card, rather than ranking optimization which assumes that "better" items should be put into top positions. Thus we take the first step to give a formal problem definition, and innovatively reduce it to Maximum Clique Optimization based on graph. To tackle this specific combinatorial optimization problem which is NP-hard, we propose Graph Attention Networks (GAttN) with a Multi-head Self-attention encoder and a decoder with attention mechanism. It can end-to-end learn the joint distribution of the K items and generate an optimal card rather than rank individual items by prediction scores. Then we propose Reinforcement Learning from Demonstrations (RLfD) which combines the advantages in behavior cloning and reinforcement learning, making it sufficientand-efficient to train the model. Extensive experiments on three datasets demonstrate the effectiveness of our proposed GAttN with RLfD method, it outperforms several strong baselines with a relative improvement of 7.7% and 4.7% on average in Precision and Hit Ratio respectively, and achieves state-of-the-art (SOTA) performance for the exact-K recommendation problem.