题目描述

Alice, who was exploring ruins in search of treasure, arrived at a corridor where the entrances to $N$ rooms were lined up in a row. Upon investigation, she found that the rooms were numbered uniquely from $1$ to $N$, but the exact number of each room was unknown until she entered. She discovered that the treasure was hidden in room $K$.

Given her remaining stamina, it was difficult for Alice to check all the rooms. However, Alice had a secret strategy to overcome this situation: binary search. Alice had successfully applied binary search to various challenges before. With her last ounce of strength, she decided to use binary search to find room $K$.

Specifically, she followed these steps:

• Initialize variables $l$ and $r$ with $l = 0$ and $r = N + 1$.
• Repeat steps 1 to 3 as follows:
  1. If $l + 1 = r$, stop the operation as she has not found room $K$.
  2. Set $m = \left\lfloor \frac{l + r}{2} \right\rfloor$. Enter the room positioned $m$-th from the left, check its number, and let this number be $x$.
  3. If $x = K$, stop the operation as she has found room $K$. If $x < K$, update $l$ to $m$. If $x > K$, update $r$ to $m$.

There are $N!$ possible mappings between rooms and numbers. You need to determine the number of mappings for which Alice can successfully find room $K$ using the above procedure, modulo $998,244,353$.

Given $T$ test cases, compute the answer for each.

输入格式

The input is given in the following format:

$$\begin{aligned} &T \\ &\text{case}_1 \\ &\text{case}_2 \\ &\vdots \\ &\text{case}_T \end{aligned} $$

Here, $\text{case}_i$ denotes the $i$-th test case.

Each test case is given in the following format:

$$N \ K$$

• $1 \leq T \leq 100,000$
• $3 \leq N \leq 10^6$
• $1 \leq K \leq N$
• All input values are integers.

输出格式

Output $T$ lines. On the $i$-th line, output the answer for the $i$-th test case.

5
3 1
4 2
5 4
10 5
1000000 314159

4
12
66
1192320
853363991