P10103 [GDKOI2023 Senior] Derangement

X has recently been studying the derangement problem, so he started thinking about a variant: how many permutations $p$ of length $n$ satisfy that for positions $i \le m$, $p_i > m$, and for all positions $i$, $p_i \ne i$? X came up with a total of $T$ such queries. Can you tell him the answer for each query? Since the answer may be too large, you only need to output it modulo $998244353$.

The first line contains an integer $T$, representing the number of queries. The next $T$ lines each contain two integers $n, m$.

Output $T$ lines, each containing one integer: the answer modulo $998244353$.

For 100% of the testdata, $0 \le T \le 2 \times 10^5$, $0 \le m \le n \le 2 \times 10^5$. This problem uses bundled subtasks. - Subtask 1 (1pts): $T = 0$. - Subtask 2 (9pts): $T \le 10$, $n, m \le 8$. - Subtask 3 (10pts): $m = 0$. - Subtask 4 (20pts): $n, m \le 5000$. - Subtask 5 (20pts): $T \le 10$. - Subtask 6 (40pts): No special constraints. Translated by ChatGPT 5