Description

Given a permutation $P$ of length $N$, you may perform the following operation any number of times: choose three positions $x, y, z \ (x<y<z)$. If $P_y<\min\{P_x,P_z\}$ or $P_y>\max\{P_x,P_z\}$, then you may delete $P_y$.

Count the number of permutations $P$ for which there exists a way to delete elements so that in the end there are at most two numbers left and $P_1=A$. Since the answer may be very large, output the result modulo $998244353$.

Input Format

The first line contains a positive integer $T$, the number of test cases.

The next $T$ lines each contain two positive integers $N, A$, representing the length of the permutation $P$ and the first number of the permutation, respectively.

Output Format

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

7
3 1
3 2
3 3
4 1
4 2
4 3
4 4

1
2
1
3
5
5
3

5
5 2
6 3
7 4
8 5
9 6

20
104
648
4662
38040

Hint

This problem uses bundled testdata.

For all testdata, it is guaranteed that $1\le T\le 10^5$ and $1\le A\le N\le 10^5$.

Translated by ChatGPT 5