D. Balancing Weaponstime limit per test3 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou've got a job in a game studio that developed an online shooter, and your first big task is to help to balance weapons. The game has n weapons: the i-th gun has an integer fire rate f_i and an integer damage per bullet d_i. The i-th gun's total firepower is equal to p_i = f_i \cdot d_i.You have to modify the values d_i of some guns in such a way that the new values d_i will still be integers, and the firepower of all guns will become balanced. Given an integer k, the guns are said to be balanced if \max\limits_{1 \le i \le n}{p_i} - \min\limits_{1 \le i \le n}{p_i} \le k.Since gamers that play your game don't like big changes, you need to change the values d_i for the minimum possible number of guns. What is the minimum number of guns for which you have to change these values to make the guns balanced?Note that the new values d_i must be integers greater than 0.InputThe first line contains a single integer t (1 \le t \le 1000) — the number of test cases.The first line of each test case contains two integers n and k (2 \le n \le 3000; 0 \le k \le 1500) — the number of guns to balance, and the maximum allowed gap between the most and the least powerful weapons.The second line contains n integers f_1, f_2, \dots, f_n (1 \le f_i \le 2000), where f_i is the fire rate of the i-th gun.The third line contains n integers d_1, d_2, \dots, d_n (1 \le d_i \le 10^9), where d_i is the damage per bullet of the i-th gun.It's guaranteed that the sum of n over all test cases doesn't exceed 3000.OutputFor each test case, print the minimum number of guns which damage d_i you have to change in order to make the guns balanced.Note that the new values d_i must be integers greater than 0.ExampleInput
54 26 3 13 71 2 1 23 2100 101 102100 99 985 01 12 4 4 312 1 3 3 42 501000 101000000000 13 51 19 1149 4 72Output
2
3
0
1
2
NoteIn the first test case, you can set d_1 = 2 and d_2 = 4. You'll get an array d = [2, 4, 1, 2], and the values of firepower will be p = [12, 12, 13, 14]. The guns are balanced, since 14 - 12 \le 2.In the second test case, you have to change the value d_i for all three guns. For example, you can set d = [5151, 5100, 5050].In the third test case, all guns are already balanced, so you don't have to change anything.
54 26 3 13 71 2 1 23 2100 101 102100 99 985 01 12 4 4 312 1 3 3 42 501000 101000000000 13 51 19 1149 4 72
2 3 0 1 2 
['binary search', 'brute force', 'data structures', 'math', 'two pointers', '*2500']