Problem Statement

You are given an integer sequence $A=(A_1,A_2,\ldots,A_N)$. Also, you are given positive integers $a,b,s,t$. It is guaranteed that $a$ and $b$ are coprime.

You can perform the following four types of operations on $A$:

• Choose an integer $i$ satisfying $1\leq i\leq N$ and add $a$ to $A_i$. This operation costs $s$.
• Choose an integer $i$ satisfying $1\leq i\leq N$ and subtract $a$ from $A_i$. This operation costs $s$.
• Choose an integer $i$ satisfying $1\leq i\leq N$ and add $b$ to $A_i$. This operation costs $t$.
• Choose an integer $i$ satisfying $1\leq i\leq N$ and subtract $b$ from $A_i$. This operation costs $t$.

Answer $Q$ queries. In the $q$-th query, you are given an integer $B_q$, so find the following value modulo $998244353$:

• The minimum total cost required to make $A_{1}=A_{2}=\cdots=A_{N}=B_q$ hold. It can be proved that it is possible to make $A_{1}=A_{2}=\cdots=A_{N}=B_q$ hold.

Constraints

• $1\leq N\leq 2\times 10^5$
• $1\leq Q\leq 2\times 10^5$
• $1\leq a,b,s,t\leq 5\times 10^8$
• $a$ and $b$ are coprime.
• $1\leq A_i\leq 5\times 10^8$
• $1\leq B_q\leq 5\times 10^8$

Input

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

N Q
a b s t
A_1 A_2 \ldots A_N
B_1 B_2 \ldots B_Q

Output

Output $Q$ values separated by spaces.

The $q$-th value should be the minimum total cost, modulo $998244353$, required to make $A_{1}=A_{2}=\cdots=A_{N}=B_q$ hold.