P13939 [EC Final 2019] Black and White

$\textit{Master Pang}$ walks from the bottom-left corner of a $n\times m$ chessboard to the top-right corner. The chessboard contains $n+1$ horizontal line segments and $m+1$ vertical line segments. The horizontal line segments are numbered from $0$ to $n$ from bottom to top and the vertical ones are numbered from $0$ to $m$ from left to right. The intersection of horizontal line segment $r$ and vertical segment $c$ is denoted by $(r,c)$. The bottom-left corner is $(0, 0)$ and the top-right corner is $(n, m)$. At each step, he can only walk from $(x, y)$ to $(x, y+1)$ or from $(x, y)$ to $(x + 1, y)$. Each of the $n\times m$ cells is colored white or black. A cell with corners $(i,j), (i+1,j), (i,j+1), (i+1,j+1)$ $(0\le i

The first line contains a single integer $T$ --- the number of test cases ($1\le T \le 100$). Each of the next $T$ lines contains three integers $n$, $m$ and $k$ ($1\le n\le 100000, 1\le m\le 100000, -100000\le k\le 100000$).

For each test case, output a single integer --- the answer modulo $998244353$.