C. Maximum Settime limit per test2 secondsmemory limit per test512 megabytesinputstandard inputoutputstandard outputA 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.InputThe 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).OutputFor 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.ExampleInput
43 1113 371 224 100Output
2 4
2 6
5 1
5 7
NoteIn 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 \}. 
43 1113 371 224 100
2 4 2 6 5 1 5 7 
['binary search', 'math', '*1600']