D. Balancing Weapons
time limit per test
3 seconds
memory limit per test
256 megabytes
input
standard input
output
standard 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 $0$.

Example
Input
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
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.