CF1671F.Permutation Counting

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 $998244353$ .