You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in python3.

Your solution must read input from standard input (cin), write output to standard output (cout).
Do not include any debug prints or additional output.

Put your final solution within a single code block:
```python
<your code here>
```

Execution time limit: 3.0 seconds
Memory limit: 512.0 MB

# Problem
You are given two arrays of integers $$$a_1, a_2, \ldots, a_n$$$ and $$$b_1, b_2, \ldots, b_n$$$. You need to handle $$$q$$$ queries of the following two types:

- $$$1$$$ $$$l$$$ $$$r$$$ $$$x$$$: assign $$$a_i := x$$$ for all $$$l \leq i \leq r$$$;
- $$$2$$$ $$$l$$$ $$$r$$$: find the minimum value of the following expression among all $$$l \leq i \leq r$$$: $$$$$$\frac{\operatorname{lcm}(a_i, b_i)}{\gcd(a_i, b_i)}.$$$$$$

In this problem $$$\gcd(x, y)$$$ denotes the greatest common divisor of $$$x$$$ and $$$y$$$, and $$$\operatorname{lcm}(x, y)$$$ denotes the least common multiple of $$$x$$$ and $$$y$$$.

## Input Format
The first line contains two integers $$$n$$$ and $$$q$$$ ($$$1 \leq n, q \leq 5 \cdot 10^4$$$) — the number of numbers in the arrays $$$a$$$ and $$$b$$$ and the number of queries.

The second line contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$1 \leq a_i \leq 5 \cdot 10^4$$$) — the elements of the array $$$a$$$.

The third line contains $$$n$$$ integers $$$b_1, b_2, \ldots, b_n$$$ ($$$1 \leq b_i \leq 5 \cdot 10^4$$$) — the elements of the array $$$b$$$.

Then $$$q$$$ lines follow, $$$j$$$-th of which starts with an integer $$$t_j$$$ ($$$1 \leq t_j \leq 2$$$) and means that the $$$j$$$-th query has type $$$t_j$$$.

If $$$t_j = 1$$$, it is followed by three integers $$$l_j$$$, $$$r_j$$$, and $$$x_j$$$ ($$$1 \leq l_j \leq r_j \leq n$$$, $$$1 \leq x_j \leq 5 \cdot 10^4$$$).

If $$$t_j = 2$$$, it is followed by two integers $$$l_j$$$ and $$$r_j$$$ ($$$1 \leq l_j \leq r_j \leq n$$$).

It is guaranteed that there is at least one query of type $$$2$$$.

## Output Format
For each query of the second type, output the minimum value of the expression.

## Examples
```input
10 10
6 10 15 4 9 25 2 3 5 30
1 2 3 4 6 9 12 15 18 30
2 1 10
1 7 10 9
2 5 10
1 1 6 14
2 4 7
2 3 9
1 2 9 30
2 1 4
2 3 7
2 5 10
```
```output
1
2
12
2
10
5
2
```
-----
```input
4 4
10 2 12 5
1 12 16 1
2 2 4
1 2 3 18
1 2 2 10
2 2 3
```
```output
5
30
```

## Note
In the first example:

- For the first query we can choose $$$i = 4$$$. So the value is $$$\frac{\operatorname{lcm}(4, 4)}{\gcd(4, 4)} = \frac{4}{4} = 1$$$.
- After the second query the array $$$a = [6, 10, 15, 4, 9, 25, 9, 9, 9, 9]$$$.
- For the third query we can choose $$$i = 9$$$. So the value is $$$\frac{\operatorname{lcm}(9, 18)}{\gcd(9, 18)} = \frac{18}{9} = 2$$$.

In the second:

- For the first query we can choose $$$i = 4$$$. So the value is $$$\frac{\operatorname{lcm}(1, 5)}{\gcd(1, 5)} = \frac{5}{1} = 5$$$.
- After the second query the array $$$a = [10, 18, 18, 5]$$$.
- After the third query the array $$$a = [10, 10, 18, 5]$$$.
- For the fourth query we can choose $$$i = 2$$$. So the value is $$$\frac{\operatorname{lcm}(10, 12)}{\gcd(10, 12)} = \frac{60}{2} = 30$$$.

Now solve the problem and return the code.