CF1633D Make Them Equal

You have an array of integers $ a $ of size $ n $ . Initially, all elements of the array are equal to $ 1 $ . You can perform the following operation: choose two integers $ i $ ( $ 1 \le i \le n $ ) and $ x $ ( $ x > 0 $ ), and then increase the value of $ a_i $ by $ \left\lfloor\frac{a_i}{x}\right\rfloor $ (i.e. make $ a_i = a_i + \left\lfloor\frac{a_i}{x}\right\rfloor $ ). After performing all operations, you will receive $ c_i $ coins for all such $ i $ that $ a_i = b_i $ . Your task is to determine the maximum number of coins that you can receive by performing no more than $ k $ operations.

The first line contains a single integer $ t $ ( $ 1 \le t \le 100 $ ) — the number of test cases. The first line of each test case contains two integers $ n $ and $ k $ ( $ 1 \le n \le 10^3; 0 \le k \le 10^6 $ ) — the size of the array and the maximum number of operations, respectively. The second line contains $ n $ integers $ b_1, b_2, \dots, b_n $ ( $ 1 \le b_i \le 10^3 $ ). The third line contains $ n $ integers $ c_1, c_2, \dots, c_n $ ( $ 1 \le c_i \le 10^6 $ ). The sum of $ n $ over all test cases does not exceed $ 10^3 $ .

For each test case, print one integer — the maximum number of coins that you can get by performing no more than $ k $ operations.