Could anyone give a solution to the problem below with $O(n\log n)$ or $O(n\log^2n)$ time plz?↵
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Given two sequences $g,h$ with length $n$ and a binary function $F(n,k)$, calculate the sequence $f$ which satisfies:↵
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$$f_{i}=\left(\sum\limits_{k=0}^{i}F(i,k)g_kh_{i-k}\right)\bmod 998244353$$↵
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And $F(n,k)$ can be **arbitrary**, such as $1$, $\binom{n}{k}$, $n^k$ or $k^n$.
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Given two sequences $g,h$ with length $n$ and a binary function $F(n,k)$, calculate the sequence $f$ which satisfies:↵
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$$f_{i}=\left(\sum\limits_{k=0}^{i}F(i,k)g_kh_{i-k}\right)\bmod 998244353$$↵
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And $F(n,k)$ can be **arbitrary**, such as $1$, $\binom{n}{k}$, $n^k$ or $k^n$.
