A15674. 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:

- $\{ 3, 6 \}$ ;
- $\{ 3, 9 \}$ ;
- $\{ 4, 8 \}$ ;
- $\{ 5, 10 \}$ .