Problem Statement

You are given a positive integer $N$ and an integer $X$.

Takahashi is at coordinate $0$ on a number line. He will now perform the following move $N$ times:

• When at coordinate $x$, choose coordinate $x-1$ or coordinate $x+1$ with equal probability and move there.

The choices of destination across the $N$ moves are all independent. Let $x'$ be the coordinate after all $N$ moves. Find the expected value, modulo $998244353$, of $|x'-X|$.

You are given $T$ test cases; solve each of them.

Definition of expected value modulo $998244353$It can be proved that the sought expected value is always a rational number. Moreover, under the constraints of this problem, it can be proved that when expressed as an irreducible fraction $\frac{P}{Q}$, we have $Q {{}\not\equiv{}} 0 \pmod{998244353}$. Therefore, there is a unique integer $R$ satisfying $R \times Q \equiv P \pmod{998244353}, 0 \leq R < 998244353$. Find this $R$.

Constraints

• $1 \leq T \leq 2 \times 10^5$
• $1 \leq N \leq 2 \times 10^5$
• $|X| \leq 2 \times 10^5$
• All input values are integers.

Input

The input is given from Standard Input in the following format:

T
\mathrm{case}_1
\mathrm{case}_2
\vdots
\mathrm{case}_T

Each $\mathrm{case}_i$ is the $i$-th test case and is given in the following format:

N X

Output

Output $T$ lines. The $i$-th line should contain the answer for the $i$-th test case.