CF2193D Monster Game

You have been gifted a new game called "Elatyh". In the game, you are given $ n $ swords, each with its own strength. In particular, the sword numbered $ i $ has a strength of $ a_i $ . The game consists of $ n $ levels, each of which features a monster. You start at level $ 1 $ and progress further. To pass level $ i $ and move on to level $ i + 1 $ , you need to defeat the monster at level $ i $ . To defeat the monster at level $ i $ , you need to deal it $ b_i $ sword strikes. The swords in the game are very fragile, so they can only deal one strike before breaking. If you complete level $ n $ or run out of swords, you can finish the game and proceed to score calculation. Before the game, you are allowed to choose the difficulty level. If you choose difficulty $ x $ , swords with a strength less than $ x $ will not affect the monsters. The game score in this case is equal to $ x $ multiplied by the number of levels completed. Your task is to choose the game difficulty in such a way as to maximize the game score.

Each test consists of several test cases. The first line contains a single integer $ t $ ( $ 1\le t\le 10^4 $ ) — the number of test cases. The following describes the test cases. The first line of each test case contains a single integer $ n $ ( $ 1\le n\le 2 \cdot 10^5 $ ). The second line of each test case contains $ n $ integers $ a_1, a_2, \dots, a_n $ $ (1\le a_i\le 10^9) $ . The third line of each test case contains $ n $ integers $ b_1, b_2, \dots, b_n $ $ (1\le b_i\le n) $ . It is guaranteed that the sum of the values of $ n $ across all test cases does not exceed $ 2 \cdot 10^5 $ .

For each test case, output a single integer — the maximum game score.

Consider the first test case. Optimal difficulty to choose is $ 3 $ . If difficulty is $ 3 $ , you can deal strikes with swords number $ 2 $ and $ 3 $ . With $ 2 $ swords you can complete $ 1 $ level, so the game score is $ 3\cdot 1 = 3 $ .