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 $ .