Solve the programming task below in a Python markdown code block.
There is an empty grid (all cells are colored white) of N rows and M columns.

Chef can fill each cell with either RED or GREEN color.  
Chef defines a *valid* path as a path of cells starting from (1,1) and ending at (N,M), where, Chef moves either right or down by 1 cell each time.

For a particular grid, Chef defines the *score* of the grid as the number of *valid* paths containing equal number of RED and GREEN cells.

Find the sum of *scores* of all possible colored grids containing N rows and M columns.  
Since the answer can be large, output it modulo 998244353.

------ Input Format ------ 

- The first line of input will contain a single integer T, denoting the number of test cases.
- Each test case consists of two integers N and M - denoting the dimensions of the grid.

------ Output Format ------ 

For each test case, output the sum of *scores* of all possible colored grids containing N rows and M columns, modulo 998244353.

------ Constraints ------ 

$1 ≤ T ≤ 1000$
$1 ≤ N, M ≤ 1000$

----- Sample Input 1 ------ 
3
1 1
1 2
2 3

----- Sample Output 1 ------ 
0
2
72

----- explanation 1 ------ 
Test case $1$: There are $2$ possible coloured grids of size $1 \times 1$. In the first grid, the one and only cell is colored RED. In the second grid, the one and only cell is colored GREEN. Neither of the grids have a *valid* path with equal number of red and green cells. Thus, score of each grid is $0$.

Test case $2$: There are $4$ possible coloured grids of the given dimension:

For grids $1$ and $4$, the scores are $0$ as there are no valid paths with equal red and green cells. Grids $2$ and $3$ have score $1$ each. The valid path with equal red and green cells is $(1,1) \rightarrow (1,2)$ in both the grids.

Thus, the sum of scores of all possible coloured grids is $2$.