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证明:

$\displaystyle\sum_{k}\left\{\begin{matrix}n+1\\k+1\end{matrix}\right\}\binom{n-k}{m-k}\left(-1\right)^{m-k}k!=\left\langle\begin{matrix}n\\m\end{matrix}\right\rangle$

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证明:

$\displaystyle\sum_{j,k} (-1)^{j+k}\binom{j+k}{k+l}\binom{r}{j}\binom{n}{k}\binom{s+n-j-k}{m-j}=\left(-1\right)^l\binom{n+r}{n+l}\binom{s-r}{m-n-l}$

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给定 $n,x,y\left(1\le n\le 10^9,0\le x,y\lt 998244353\right)$，多组询问 $a,b$，求

$$ \sum_{i=a}^{n}\binom{i}{a}x^{i-a}\binom{n-i}{b}y^{n-i-b}\pmod{998244353} $$

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