P4831 Scarlet Loves WenHuaKe

Scarlet has started college. Before that, she worked hard on a Gaokao mock exam problem QAQ.

Scarlet tries to place $2\times n$ cannons on an $n$-row $m$-column Chinese chessboard such that none of them can attack each other. As everyone knows, Scarlet loves making trouble. She wants to ask how many valid configurations there are.

One line with two integers, representing $n$ and $m$.

One integer, the number of configurations modulo $998244353$.

For $20\%$ of the testdata, $n,m\leq5$. For another $25\%$ of the testdata, $n,m\leq2000$. For another $20\%$ of the testdata, $n=m$. For the remaining $35\%$ of the testdata, $m-n\leq10$. For $100\%$ of the testdata, $1\leq n\leq m\leq100000$. Translated by ChatGPT 5