CF1796C Maximum Set

A set of positive integers $ S $ is called beautiful if, for every two integers $ x $ and $ y $ from this set, either $ x $ divides $ y $ or $ y $ divides $ x $ (or both). You are given two integers $ l $ and $ r $ . Consider all beautiful sets consisting of integers not less than $ l $ and not greater than $ r $ . You have to print two numbers: - the maximum possible size of a beautiful set where all elements are from $ l $ to $ r $ ; - the number of beautiful sets consisting of integers from $ l $ to $ r $ with the maximum possible size. Since the second number can be very large, print it modulo $ 998244353 $ .

The first line contains one integer $ t $ ( $ 1 \le t \le 2 \cdot 10^4 $ ) — the number of test cases. Each test case consists of one line containing two integers $ l $ and $ r $ ( $ 1 \le l \le r \le 10^6 $ ).

For each test case, print two integers — the maximum possible size of a beautiful set consisting of integers from $ l $ to $ r $ , and the number of such sets with maximum possible size. Since the second number can be very large, print it modulo $ 998244353 $ .

In the first test case, the maximum possible size of a beautiful set with integers from $ 3 $ to $ 11 $ is $ 2 $ . There are $ 4 $ such sets which have the maximum possible size: - $ \{ 3, 6 \} $ ; - $ \{ 3, 9 \} $ ; - $ \{ 4, 8 \} $ ; - $ \{ 5, 10 \} $ .