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If $l$ is not a power of 2 and $f(0)=1$, Gathen and Gerhard suggest to compute the inverse,$f^{-1}$, modulo $x^{\\lceil l/2^r\\rceil}, x^{\\lceil l/2^{r-1}\\rceil},..., x^{\\lceil l/2\\rceil}, x^l$, separately. But they did not specify the iterative step. 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