Luca is in front of a row of $$$n$$$ trees. The $$$i$$$-th tree has $$$a_i$$$ fruit and height $$$h_i$$$.

He wants to choose a contiguous subarray of the array $$$[h_l, h_{l+1}, \dots, h_r]$$$ such that for each $$$i$$$ ($$$l \leq i \lt r$$$), $$$h_i$$$ is divisible$$$^{\dagger}$$$ by $$$h_{i+1}$$$. He will collect all the fruit from each of the trees in the subarray (that is, he will collect $$$a_l + a_{l+1} + \dots + a_r$$$ fruits). However, if he collects more than $$$k$$$ fruits in total, he will get caught.

What is the maximum length of a subarray Luca can choose so he doesn't get caught?

$$$^{\dagger}$$$ $$$x$$$ is divisible by $$$y$$$ if the ratio $$$\frac{x}{y}$$$ is an integer.

Input

The first line contains a single integer $$$t$$$ ($$$1 \leq t \leq 1000$$$) — the number of test cases.

The first of each test case line contains two space-separated integers $$$n$$$ and $$$k$$$ ($$$1 \leq n \leq 2 \cdot 10^5$$$; $$$1 \leq k \leq 10^9$$$) — the number of trees and the maximum amount of fruits Luca can collect without getting caught.

The second line of each test case contains $$$n$$$ space-separated integers $$$a_i$$$ ($$$1 \leq a_i \leq 10^4$$$) — the number of fruits in the $$$i$$$-th tree.

The third line of each test case contains $$$n$$$ space-separated integers $$$h_i$$$ ($$$1 \leq h_i \leq 10^9$$$) — the height of the $$$i$$$-th tree.

The sum of $$$n$$$ over all test cases does not exceed $$$2 \cdot 10^5$$$.

Output

For each test case output a single integer, the length of the maximum length contiguous subarray satisfying the conditions, or $$$0$$$ if there is no such subarray.

Note

In the first test case, Luca can select the subarray with $$$l=1$$$ and $$$r=3$$$.

In the second test case, Luca can select the subarray with $$$l=3$$$ and $$$r=4$$$.

In the third test case, Luca can select the subarray with $$$l=2$$$ and $$$r=2$$$.

Money Trees

Examples