Description:
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$$$.
Output Format:
For each query of the second type, output the minimum value of the expression.
Note:
In the first example:
- For the first query we can choose $$$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$$$.