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Contest: Task: Related: TaskG TaskI

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.

Sample Input 1

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

Sample Output 1

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 $a_1 + a_2 + a_3 = 3 + 3 + 3 = 9$.

Sample Input 2

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

Sample Output 2

51
12
33
26
132