Problem Statement

Given are integers $N$ and $A$. Find the number, modulo $998244353$, of permutations $P=(P_1,P_2,\cdots,P_N)$ of $(1,2,\cdots,N)$ that satisfy the following conditions.

• $P_1=A$.
• It is possible to repeat the following operation so that $P$ has just two elements.
• Choose three consecutive elements $x$, $y$, and $z$. Here, $y<\min(x,z)$ or $y>\max(x,z)$ must hold. Then, erase $y$ from $P$.

Solve $T$ test cases in an input file.

Constraints

• $1 \leq T \leq 5 \times 10^5$
• $3 \leq N \leq 10^6$
• $1 \leq A \leq N$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

T
case_1
case_2
\vdots
case_T

Each case is in the following format:

N A

Output

Print the answer for each test case.