Two Sequence Queries

题目描述

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 $998244353$.

输入格式

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

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

$3$ $l$ $r$

输出格式

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.

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

16
25
84

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

716070898
151723988

提示

$1\leq N,Q\leq 2\times 10^5$ $0\leq A_i,B_i\leq 10^9$ $1\leq l\leq r\leq N$ $1\leq x\leq 10^9$ All input values are integers. There is at least one query of the third type.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.
Make sure to print the sum modulo $998244353$ for the third type of query.

标签: AtCoder|abc357F

来源

AtCoder|abc357F