8566: The Pool

链接：https://ac.nowcoder.com/acm/contest/33192/D
来源：牛客网
Marisa wants to build an $n\times m$ rectangular swimming pool for Alice. To do this, Marisa can select four integral points on an infinite 2D-grid and cast magic. For example, the following picture shows three possible ways to build a $5\times 5$ swimming pool.



Marisa soon learns that there are many ways to build the pool since four sides of the pool can be non-parallel to coordinate axis. Here two ways are considered different if and only if the pool in one way can't be translated (moved without rotation and flipping) to the pool in the other way. Now Marisa becomes curious about the total numbers of complete $1\times 1$ squares inside the pool for all possible ways. As the result can be very large, you should print it modulo $998244353$.

In the first line, there is one integer $T$ (1≤T≤1041\leq T\leq 10^41≤T≤104), denoting the number of test cases.
For each test case, there is one line containing two numbers $n$ and $m$ (1≤n,m≤10181\leq n,m\leq 10^{18}1≤n,m≤1018), denotes the size of swimming pool.
It is guaranteed that there are at most 10 cases that max(n,m)>109max(n,m) > 10^9max(n,m)>109.

For each test case, print one number, denoting the total number of complete $1\times 1$ squares inside the pool for all possible ways (modulo $998244353$).).

5
5 5
2 3
5 10
2197525579 1145141
91 65

51
12
228
438744975
34722