Score : $600$ points

Problem Statement

You are given $N$, $Q$, and $A=(a_1,\ldots,a_N)$. Process $Q$ queries described below. Each query is of one of the following three kinds:

• 1 L R x: for $i=L,L+1,\dots,R$, update the value of $a_i$ to $\displaystyle \left\lfloor \frac{a_i}{x} \right\rfloor$.
• 2 L R y: for $i=L,L+1,\dots,R$, update the value of $a_i$ to $y$.
• 3 L R: print $\displaystyle\sum_{i=L}^R a_i$.

Constraints

• $1 \leq N \leq 5 \times 10^5$
• $1 \leq Q \leq 10^5$
• $1 \leq L \leq R \leq N$
• $1 \leq a_i \leq 10^5$
• $2 \leq x \leq 10^5$
• $1 \leq y \leq 10^5$
• All values in input are integers.

Input

Input is given from Standard Input in the following format, where $\text{query}_i$ denotes the $i$-th query to be processed:

$N$ $Q$

$a_1$ $a_2$ $\dots$ $a_N$

$\text{query}_1$

$\text{query}_2$

$\vdots$

$\text{query}_Q$

Each query is given in one of the following three formats:

$1$ $L$ $R$ $x$

$2$ $L$ $R$ $y$

$3$ $L$ $R$

Output

Print the answer to the queries as specified in the Problem Statement, with newlines in between.

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

13
4
9

Initially, $A = (2, 5, 6)$. Thus, the answer to the $1$-st query is $a_1 + a_2 + a_3 = 2 + 5 + 6 = 13$. When the $2$-nd query has been processed, $A = (2, 2, 3)$. Thus, the answer to the $3$-rd query is $a_1 + a_2 = 2 + 2 = 4$. When the $4$-th query has been processed, $A = (3, 3, 3)$. Thus, the answer to the $5$-th query is $a_1 + a_2 + a_3 = 3 + 3 + 3 = 9$.

6 11
10 3 5 20 6 7
3 1 6
1 2 4 3
3 1 3
2 1 4 10
3 3 6
1 3 6 2
2 1 4 5
3 1 6
2 1 3 100
1 2 5 6
3 1 4

51
12
33
26
132