Score : $550$ points

问题陈述

你得到了两个长度为 $N$ 的序列，$A=(A_1,A_2,\ldots,A_N)$ 和 $B=(B_1,B_2,\ldots,B_N)$。 你还需要按顺序处理 $Q$ 个查询。

有三种类型的查询：

• 1 l r x : 将 $x$ 加到 $A_l, A_{l+1}, \ldots, A_r$ 的每一个元素上。
• 2 l r x : 将 $x$ 加到 $B_l, B_{l+1}, \ldots, B_r$ 的每一个元素上。
• 3 l r : 打印 $\displaystyle\sum_{i=l}^r (A_i\times B_i)$ 除以 $998244353$ 后的余数。

以上为大语言模型 kimi 翻译，仅供参考。

Problem Statement

You are given sequences of length $N$, $A=(A_1,A_2,\ldots,A_N)$ and $B=(B_1,B_2,\ldots,B_N)$.
You are also given $Q$ queries to process in order.

There are three types of queries:

• 1 l r x : Add $x$ to each of $A_l, A_{l+1}, \ldots, A_r$.
• 2 l r x : Add $x$ to each of $B_l, B_{l+1}, \ldots, B_r$.
• 3 l r : Print the remainder of $\displaystyle\sum_{i=l}^r (A_i\times B_i)$ when divided by $998244353$.

Constraints

• $1\leq N,Q\leq 2\times 10^5$
• $0\leq A_i,B_i\leq 10^9$
• $1\leq l\leq r\leq N$
• $1\leq x\leq 10^9$
• All input values are integers.
• There is at least one query of the third type.

Input

The input is given from Standard Input in the following format. Here, $\mathrm{query}_i$ $(1\leq i\leq Q)$ is the $i$-th query to be processed.

$N$ $Q$

$A_1$ $A_2$ $\ldots$ $A_N$

$B_1$ $B_2$ $\ldots$ $B_N$

$\mathrm{query}_1$

$\mathrm{query}_2$

$\vdots$

$\mathrm{query}_Q$

Each query is given in one of the following formats:

$1$ $l$ $r$ $x$

$2$ $l$ $r$ $x$

$3$ $l$ $r$

Output

If there are $K$ queries of the third type, print $K$ lines.
The $i$-th line ($1\leq i\leq K$) should contain the output for the $i$-th query of the third type.

Sample Input 1

5 6
1 3 5 6 8
3 1 2 1 2
3 1 3
1 2 5 3
3 1 3
1 1 3 1
2 5 5 2
3 1 5

Sample Output 1

16
25
84

Initially, $A=(1,3,5,6,8)$ and $B=(3,1,2,1,2)$. The queries are processed in the following order:

• For the first query, print $(1\times 3)+(3\times 1)+(5\times 2)=16$ modulo $998244353$, which is $16$.
• For the second query, add $3$ to $A_2,A_3,A_4,A_5$. Now $A=(1,6,8,9,11)$.
• For the third query, print $(1\times 3)+(6\times 1)+(8\times 2)=25$ modulo $998244353$, which is $25$.
• For the fourth query, add $1$ to $A_1,A_2,A_3$. Now $A=(2,7,9,9,11)$.
• For the fifth query, add $2$ to $B_5$. Now $B=(3,1,2,1,4)$.
• For the sixth query, print $(2\times 3)+(7\times 1)+(9\times 2)+(9\times 1)+(11\times 4)=84$ modulo $998244353$, which is $84$.

Thus, the first, second, and third lines should contain $16$, $25$, and $84$, respectively.

Sample Input 2

2 3
1000000000 1000000000
1000000000 1000000000
3 1 1
1 2 2 1000000000
3 1 2

Sample Output 2

716070898
151723988

Make sure to print the sum modulo $998244353$ for the third type of query.