Adachi is in the middle of a generational crashout... over, uh, this problem! Yep, that's definitely it... anyways, please help her solve it! You are given two arrays (a) and (b) of length (n) ((1\leq a_i\leq b_i)). In one operation, you may either: choose an index (i) ((1\leq i\leq n)) and set (a_i := a_i + 1), or double all elements of (a). Let (x) denote the minimum number of operations needed to make (a = b). Two arrays (a) and (b) of length (n) are considered equal if (a_i = b_i) for all (1\leq i\leq n). Find the value of (x). Additionally, count the number of sequences of operations that make (a = b) using exactly (x) operations. Two such sequences of operations are considered different if, for any (1\leq j\leq x), the (j)-th operation of each sequence differs (either in the type of operation selected or the index chosen, if applicable). Since the number of sequences may be large, output it modulo ({\color{red}{10^6+3}}). Note that (10^6+3) is a prime number. The first line contains a single integer (t) ((1\leq t\leq 10^4)) — the number of test cases. The first line of each test case contains a single integer (n) ((2\leq n\leq 2\cdot 10^5)). The second line of each test case contains (n) integers, (a_1, a_2, \dots, a_n) ((1\leq a_i\leq 10^6)). The third line of each test case contains (n) integers, (b_1, b_2, \dots, b_n) ((a_i\leq b_i\leq 10^6)). It is guaranteed that the sum of (n) over all test cases does not exceed (2\cdot 10^5). For each test case, output two integers, the value of (x), and the number of sequences of operations that make (a = b) using exactly (x) operations, modulo (10^6+3). The value of (x) should be printed exactly; that is, it should not be taken modulo (10^6 + 3). In the second sample, it is possible to convert (a) into (b) using only three operations. There is