AT_arc210_f [ARC210F] ± ab

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.

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 $ 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.

### Sample Explanation 1 - By performing operations $ +a $ , $ -b $ on $ A_1 $ in order, we can make $ A=(1) $ . The total cost is $ 4+3=7 $ . - By performing operations $ -a $ , $ -a $ , $ +b $ on $ A_1 $ in order, we can make $ A=(2) $ . The total cost is $ 4+4+3=11 $ . - $ A=(3) $ from the beginning. The total cost is $ 0 $ . - By performing operations $ +a $ , $ +a $ , $ -b $ on $ A_1 $ in order, we can make $ A=(4) $ . The total cost is $ 4+4+3=11 $ . - By performing operations $ -a $ , $ +b $ on $ A_1 $ in order, we can make $ A=(5) $ . The total cost is $ 4+3=7 $ . ### Sample Explanation 2 - By performing operations $ +a $ on $ A_1 $ , $ +b $ , $ -a $ on $ A_2 $ , and $ +a,+a,-b $ on $ A_3 $ in order, we can make $ A=(4,4,4) $ . The total cost is $ 22 $ . ### 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 $