Problem Statement

There is a grid with H rows and W columns.
This grid has H(W+1) vertical edges and W(H+1) horizontal edges, for a total of H(W+1) + W(H+1) (see also the figures at Sample Input/Output). Consider marking these edges by the following two kinds of operations.

• Operation (1): Choose a square whose left and upper edges are unmarked when performing this operation. Mark the left and upper edges of that square.
• Operation (2): Choose a square whose right and lower edges are unmarked when performing this operation. Mark the right and lower edges of that square.

Find the number, modulo 998244353, of possible sets of edges that are eventually marked when Operations (1) and (2) can be performed any number of times, possibly zero.
You have T test cases to solve.

Input

The input is given from Standard Input in the following format:
T
$\text{case}_1$
$\vdots$
$\text{case}_T$

Each test case is given in the following format:
H W

Output

Print T lines. The i-th line should contain the number, modulo 998244353, of possible sets of edges that are eventually marked for the i-th test case.

Constraints

• $1\leq T\leq 2\times 10^5$
• $1\leq H, W\leq 10^6$

Sample Input 1

2
1 1
2 3

Sample Output 1

4
800

For the case (H, W)=(1,1), there are four possible sets of edges that are eventually marked, as shown below. The marked edges are drawn in bold.

For the case (H, W)=(2,3), the following sets of marked edges are possible:

On the other hand, the following sets of marked edges are impossible:

Sample Input 2

3
123 456
654 321
1000000 1000000

Sample Output 2

60549740
298307903
656009181

见题面 Input 部分

见题面 Output 部分