A15003. Permutation Counting
编程题
普及/提高-
知识点
题目描述
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!
Yep, that's the whole problem. Good luck!
输入格式
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 $x$ ( $1 \le n \le 998244352$ ; $1 \le k \le 11$ ; $1 \le x \le 11$ ).
Each test case consists of one line which contains three integers $n$ , $k$ and $x$ ( $1 \le n \le 998244352$ ; $1 \le k \le 11$ ; $1 \le x \le 11$ ).
输出格式
For each test case, print one integer — the answer to the problem, taken modulo $998244353$ .
输入输出样例
输入 #1
5 10 6 4 7 3 1 163316 11 7 136373 11 1 325902 11 11
输出 #1
465 12 986128624 7636394 57118194