Two Sequence Queries

AtCoder

IDabc357_f

Time5000ms

Memory256MB

Difficulty—

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: $1$ $l$ $r$ $x$ $2$ $l$ $r$ $x$ $3$ $l$ $r$ [samples]

Samples

Input #1

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.

Input #2

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

Output #2

716070898
151723988

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

API Response (JSON)

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    "name": "Two Sequence Queries",
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      "content": "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` : A",
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      "statement_type": "Markdown",
      "content": "You are given sequences of length $N$, $A=(A_1,A_2,\\ldots,A_N)$ and $B=(B_1,B_2,\\ldots,B_N)$.  \nYou are also given $Q$ queries to process in order.\nThere are three types of queries:\n\n*   `1 l r x` : A...",
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