F. Permutation Countingtime limit per test4 secondsmemory limit per test512 megabytesinputstandard inputoutputstandard outputCalculate 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!InputThe 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).OutputFor each test case, print one integer — the answer to the problem, taken modulo 998244353.ExampleInput
5
10 6 4
7 3 1
163316 11 7
136373 11 1
325902 11 11
Output
465
12
986128624
7636394
57118194

5
10 6 4
7 3 1
163316 11 7
136373 11 1
325902 11 11

465 12 986128624 7636394 57118194 
['brute force', 'combinatorics', 'dp', 'fft', 'math', '*2700']