A16223 | Money Trees

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 $i$ ( $l \leq i < r$ ), $h_i$ 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.

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 $2 \cdot 10^5$ .

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.