Simple Math Problem

Given two positive integers $m$ and $n$, compute the following value modulo 998244353:

$\sum_{i=0}^{\lfloor m/2 \rfloor} \sum_{j=0}^{\lfloor n/2 \rfloor} \binom{i+j}{j}^2 \binom{m+n-2i-2j}{n-2j}$

Here, $\binom{a}{b}$ is the binomial coefficient, the number of ways to choose an unordered subset of $b$ items from a fixed set of $a$ items.

The first line contains one integer $T$ ($1 \le T \le 10^5$), the number of test cases. Each test case is a single line containing two integers $m$ and $n$ ($1 \le m, n \le 10^5$).

For each test case, output one line containing the value of the formula modulo 998244353.