Score : $1000$ points

Problem Statement

Snuke and $N+M$ children are standing on a number line.

At time $0$, they are at the following positions.

• Snuke is at coordinate $0$.
• $N$ children are at negative coordinates. The $i$-th of them is at coordinate $-L_i$.
• $M$ children are at positive coordinates. The $i$-th of them is at coordinate $R_i$.

They will now play a game of tag. Specifically, they will do the following actions.

• Snuke first chooses a string $s$ consisting of $N$ Ls and $M$ Rs. Then, for each $i=1,2,\cdots,N+M$, he does the following.- If the $i$-th character of $s$ is L, start moving at a speed of $2$ in the negative direction.
  • If the $i$-th character of $s$ is R, start moving at a speed of $2$ in the positive direction.
  • When having caught a child (by occupying the same coordinate), go to the next $i$, or end the game if $i=N+M$.
• If the $i$-th character of $s$ is L, start moving at a speed of $2$ in the negative direction.
• If the $i$-th character of $s$ is R, start moving at a speed of $2$ in the positive direction.
• When having caught a child (by occupying the same coordinate), go to the next $i$, or end the game if $i=N+M$.
• Every child keeps moving at a speed of $1$ in the direction away from Snuke.

Assume that we have found the time when the game ends for every $s$ that Snuke can choose in the beginning. Find the sum of all those values, modulo $998244353$.

Constraints

• $3 \leq N,M \leq 250000$
• $1 \leq L_1 < L_2 < \cdots < L_N < 998244353$
• $1 \leq R_1 < R_2 < \cdots < R_M < 998244353$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$ $M$

$L_1$ $L_2$ $\cdots$ $L_N$

$R_1$ $R_2$ $\cdots$ $R_M$

Output

Print the answer.

3 3
1 2 3
1 2 3

2748

For example, if $s=$LRRLLR, the game goes as follows.

• At time $0$: Snuke starts moving in the negative direction.
• At time $1$: Snuke catches a child at coordinate $-2$ and starts moving in the positive direction.
• At time $5$: Snuke catches a child at coordinate $6$ and starts moving in the positive direction.
• At time $6$: Snuke catches a child at coordinate $8$ and starts moving in the negative direction.
• At time $22$: Snuke catches a child at coordinate $-24$ and starts moving in the negative direction.
• At time $23$: Snuke catches a child at coordinate $-26$ and starts moving in the positive direction.
• At time $75$: Snuke catches a child at coordinate $78$ and ends the game.

7 5
89789743 196247866 205535557 542612813 782887985 889864096 899373580
539329402 618885430 714090971 717251433 860233092

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