Calculate the number of permutations $$$p$$$ of size $$$n$$$ with exactly $$$k$$$ inversions (pairs of indices $$$(i, j)$$$ such that $$$i < j$$$ and $$$p_i > p_j$$$) and exactly $$$x$$$ indices $$$i$$$ such that $$$p_i > p_{i+1}$$$.
Yep, that's the whole problem. Good luck!
The first line contains one integer $$$t$$$ ($$$1 \le t \le 3 \cdot 10^4$$$) — the number of test cases.
Each test case consists of one line which contains three integers $$$n$$$, $$$k$$$ and $$$x$$$ ($$$1 \le n \le 998244352$$$; $$$1 \le k \le 11$$$; $$$1 \le x \le 11$$$).
For each test case, print one integer — the answer to the problem, taken modulo $$$998244353$$$.
510 6 47 3 1163316 11 7136373 11 1325902 11 11
465 12 986128624 7636394 57118194
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