Sequence Operations and Queries

Given two sequences of integers, \(a_i\) and \(b_i\), each of length \(n\), you need to process \(q\) queries of three types:

1. Update by condition: Given an interval \([l, r]\) and two integers \(k\) and \(t\), for each index \(i\) in \([l, r]\) (1-indexed) such that \(a_i \times b_i \le k\) (i.e. \(a_i \times b_i \leq k\)), add \(t\) to both \(a_i\) and \(b_i\).
2. Point update: Given an index \(i\) and two integers \(x\) and \(y\), update \(a_i = x\) and \(b_i = y\).
3. Range query: Given an interval \([l, r]\), output the sum \(\sum_{i=l}^{r} (a_i+b_i)\).

All indices in the queries are 1-indexed.

Note: The constraints are such that a straightforward simulation is acceptable.

inputFormat

The first line contains two integers \(n\) and \(q\) -- the length of the sequences and the number of queries.

The second line contains \(n\) integers representing the sequence \(a_1, a_2, \ldots, a_n\).

The third line contains \(n\) integers representing the sequence \(b_1, b_2, \ldots, b_n\).

The next \(q\) lines each represent a query in one of the following formats:

• For query type 1: 1 l r k t
• For query type 2: 2 i x y
• For query type 3: 3 l r

outputFormat

For each query of type 3, output the corresponding sum \(\sum_{i=l}^{r} (a_i+b_i)\) on a separate line.

sample

5 5
1 2 3 4 5
5 4 3 2 1
3 1 5
1 2 4 10 1
3 1 5
2 3 10 10
3 1 5

30
35
48