CF1796C.Maximum Set
普及/提高-
通过率:0%
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题目描述
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 .
输入格式
The first line contains one integer t ( 1≤t≤2⋅104 ) — the number of test cases.
Each test case consists of one line containing two integers l and r ( 1≤l≤r≤106 ).
输出格式
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 .
输入输出样例
输入#1
4 3 11 13 37 1 22 4 100
输出#1
2 4 2 6 5 1 5 7
说明/提示
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} .