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The main contribution of this paper is the upper bound: $\\pi\\left(n, K^{(k)}_{g}, K^{(k)}_r\\right) \\leq \\left(1 + O\\left(n^{-1}\\right) \\right)\\prod_{m=k}^{g} \\left(1 - \\frac{\\binom{m-1}{k-1}}{\\binom{r-1}{k-1}} \\right).$ The graph case ($k=2$) is the first known generalized Tur\\'an question, investigated by Erd\\H{o}s. 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