Periodical Numbers
题意翻译
求出$[l,r]$之间所有满足二进制表示存在循环节的数的个数。
$s_{1..n}$有长度为$k$的循环节,当且仅当:
1. $n$是$k$的倍数
2. 对于所有$1\le i\le n - k$,条件$s_i = s_{i +k}$均成立。
题目描述
A non-empty string $ s $ is called binary, if it consists only of characters "0" and "1". Let's number the characters of binary string $ s $ from 1 to the string's length and let's denote the $ i $ -th character in string $ s $ as $ s_{i} $ .
Binary string $ s $ with length $ n $ is periodical, if there is an integer $ 1<=k<n $ such that:
- $ k $ is a divisor of number $ n $
- for all $ 1<=i<=n-k $ , the following condition fulfills: $ s_{i}=s_{i+k} $
For example, binary strings "101010" and "11" are periodical and "10" and "10010" are not.
A positive integer $ x $ is periodical, if its binary representation (without leading zeroes) is a periodic string.
Your task is to calculate, how many periodic numbers are in the interval from $ l $ to $ r $ (both ends are included).
输入输出格式
输入格式
The single input line contains two integers $ l $ and $ r $ ( $ 1<=l<=r<=10^{18} $ ). The numbers are separated by a space.
Please, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.
输出格式
Print a single integer, showing how many periodic numbers are in the interval from $ l $ to $ r $ (both ends are included).
输入输出样例
输入样例 #1
1 10
输出样例 #1
3
输入样例 #2
25 38
输出样例 #2
2
说明
In the first sample periodic numbers are $ 3 $ , $ 7 $ and $ 10 $ .
In the second sample periodic numbers are $ 31 $ and $ 36 $ .