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