CF1873F 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.

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 $ .