F. Permutation Counting
time limit per test
4 seconds
memory limit per test
512 megabytes
input
standard input
output
standard output

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!

Input

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 $$$x$$$ ($$$1 \le n \le 998244352$$$; $$$1 \le k \le 11$$$; $$$1 \le x \le 11$$$).

Output

For each test case, print one integer — the answer to the problem, taken modulo $$$998244353$$$.

Example
Input
5
10 6 4
7 3 1
163316 11 7
136373 11 1
325902 11 11
Output
465
12
986128624
7636394
57118194