E. Locationtime limit per test3 secondsmemory limit per test512 megabytesinputstandard inputoutputstandard outputYou 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.InputThe 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.OutputFor each query of the second type, output the minimum value of the expression.ExamplesInput
10 106 10 15 4 9 25 2 3 5 301 2 3 4 6 9 12 15 18 302 1 101 7 10 92 5 101 1 6 142 4 72 3 91 2 9 302 1 42 3 72 5 10Output
1
2
12
2
10
5
2
Input
4 410 2 12 51 12 16 12 2 41 2 3 181 2 2 102 2 3Output
5
30
NoteIn 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. 
10 106 10 15 4 9 25 2 3 5 301 2 3 4 6 9 12 15 18 302 1 101 7 10 92 5 101 1 6 142 4 72 3 91 2 9 302 1 42 3 72 5 10
1 2 12 2 10 5 2 
['data structures', 'dp', 'math', 'number theory', '*2800']