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I need to find the first $n$ coefficients of $$\prod_{i = 1}^{i = q}(1 + x^{a_i})^{b_i}$$ modulo a NTT favourable prime. Can someone suggest an algorithm with worst-case complexity $O(n\log n)$ or $O(q\log q)$? I think this is to be done using NTT but cannot get an exact method. I tried Divide and Conquer but it is $O(qn\log n)$.

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