310316: CF1814D. Balancing Weapons

D. Balancing Weaponstime limit per test3 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard output

You'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 $0$.

Input

The 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 $3000$.

Output

For 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

5
4 2
6 3 13 7
1 2 1 2
3 2
100 101 102
100 99 98
5 0
1 12 4 4 3
12 1 3 3 4
2 50
1000 10
1000000000 1
3 5
1 19 11
49 4 72

Output

2
3
0
1
2

Note

In 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.

题目大意：
你在一个游戏工作室工作，负责平衡一款在线射击游戏中的武器。游戏中有n把武器，第i把武器的射速为f_i，每颗子弹的伤害为d_i。每把武器的火力值为p_i = f_i * d_i。你的任务是修改某些武器的d_i值，使得所有武器的火力值平衡。给定整数k，如果max(p_i) - min(p_i) <= k，则认为武器平衡。要求改变d_i的最小数量，并保证新的d_i为大于0的整数。

输入数据格式：
第一行包含一个整数t（1 ≤ t ≤ 1000），表示测试用例的数量。
每个测试用例的第一行包含两个整数n和k（2 ≤ n ≤ 3000；0 ≤ k ≤ 1500），分别表示要平衡的武器数量和最大允许的火力值差距。
每个测试用例的第二行包含n个整数f_1, f_2, ..., f_n（1 ≤ f_i ≤ 2000），表示每把武器的射速。
每个测试用例的第三行包含n个整数d_1, d_2, ..., d_n（1 ≤ d_i ≤ 10^9），表示每把武器的每颗子弹伤害。
保证所有测试用例的n之和不超过3000。

输出数据格式：
对于每个测试用例，输出一个整数，表示为了使武器平衡，需要改变的最小武器数量。

示例：
输入：
5
4 2
6 3 13 7
1 2 1 2
3 2
100 101 102
100 99 98
5 0
1 12 4 4 3
12 1 3 3 4
2 50
1000 10
1000000000 1
3 5
1 19 11
49 4 72
输出：
2
3
0
1
2题目大意： 你在一个游戏工作室工作，负责平衡一款在线射击游戏中的武器。游戏中有n把武器，第i把武器的射速为f_i，每颗子弹的伤害为d_i。每把武器的火力值为p_i = f_i * d_i。你的任务是修改某些武器的d_i值，使得所有武器的火力值平衡。给定整数k，如果max(p_i) - min(p_i) <= k，则认为武器平衡。要求改变d_i的最小数量，并保证新的d_i为大于0的整数。 输入数据格式： 第一行包含一个整数t（1 ≤ t ≤ 1000），表示测试用例的数量。 每个测试用例的第一行包含两个整数n和k（2 ≤ n ≤ 3000；0 ≤ k ≤ 1500），分别表示要平衡的武器数量和最大允许的火力值差距。 每个测试用例的第二行包含n个整数f_1, f_2, ..., f_n（1 ≤ f_i ≤ 2000），表示每把武器的射速。 每个测试用例的第三行包含n个整数d_1, d_2, ..., d_n（1 ≤ d_i ≤ 10^9），表示每把武器的每颗子弹伤害。 保证所有测试用例的n之和不超过3000。 输出数据格式： 对于每个测试用例，输出一个整数，表示为了使武器平衡，需要改变的最小武器数量。 示例： 输入： 5 4 2 6 3 13 7 1 2 1 2 3 2 100 101 102 100 99 98 5 0 1 12 4 4 3 12 1 3 3 4 2 50 1000 10 1000000000 1 3 5 1 19 11 49 4 72 输出： 2 3 0 1 2