Description

Input

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

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

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

4 4
10 2 12 5
1 12 16 1
2 2 4
1 2 3 18
1 2 2 10
2 2 3

1
2
12
2
10
5
2

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 $\frac{\operatorname{lcm}(10, 12)}{\gcd(10, 12)} = \frac{60}{2} = 30$.