P10588 "ALFR Round 2" D Hypercube.

> What comes into view is a huge cherry blossom tree. > > Under the tree stands a girl, looking up at it. > I think: She is probably a freshman. Maybe, like me, she also sneaked out. > I also look up at that cherry blossom tree. The blurry colors of the blossoms cover the sky. > A gust of wind rises, and the dancing cherry blossom petals wrap around the girl. > The girl also sees me...

That was your first encounter with Milja. As always, Milja gives you another sequence problem. The white envelope carries a scent of citrus, and you carefully open it and read. ------------ In 3D, we have a cube. The coordinates of its $2^3$ vertices can all be written in the form $(x,y,z)$. Similarly, in $n$ dimensions, we have an $n$-dimensional hypercube with $2^n$ vertices. Its edge length is $1$, and every coordinate of every vertex is a non-negative integer. Starting from the point $(0,0,\dots,0)$, you walk along $m$ edges. Find the total number of ways to arrive at the point $(1,1,\dots,0)$. Among the coordinates of the destination point, there are $l$ digits equal to $1$. Since the answer may be very large, you only need to output the result modulo $998244353$.

The first line contains an integer $T$, which denotes the number of test cases. The next $T$ lines each contain three non-negative integers $n,m,l$.

For each test case, output one line containing one integer: the answer.

### Sample Explanation The $7$ ways in the first example are: - $(0,0,0) \to (1,0,0) \to (0,0,0) \to (1,0,0)$ - $(0,0,0) \to (0,1,0) \to (0,0,0) \to (1,0,0)$ - $(0,0,0) \to (0,0,1) \to (0,0,0) \to (1,0,0)$ - $(0,0,0) \to (1,0,0) \to (1,1,0) \to (1,0,0)$ - $(0,0,0) \to (1,0,0) \to (1,0,1) \to (1,0,0)$ - $(0,0,0) \to (0,1,0) \to (1,1,0) \to (1,0,0)$ - $(0,0,0) \to (0,0,1) \to (1,0,1) \to (1,0,0)$ ### Constraints | Subtask | Points | Constraints | | :----------: | :----------: | :----------: | | $0$ | $10$ | $\sum nm\le2^{26}$, $n\le2^{13}$ | | $1$ | $20$ | $l=0$ | | $2$ | $30$ | $\sum n^2\le2^{26}$ | | $3$ | $40$ | - | For $100\%$ of the testdata: $1\le T\le600$, $\sum n\log_2 n\le2^{25}$, $n\in[1,2^{21}]$, $m\in[0,2^{64}-1]$, $l\in[0,n]$. --- You turn to the back and find a line of small text: Please do not forget to consider special cases. Translated by ChatGPT 5