Maximum Set

2000ms

524288K

Description:

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 $$$998244353$$$.

Input:

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 $$$r$$$ ($$$1 \le l \le r \le 10^6$$$).

Output:

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 $$$998244353$$$.

Sample Input:

Sample Output:

Note:

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:

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

Informação

Provedor Codeforces

Código CF1796C