A8577. Periodical Numbers

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).

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.

Print a single integer, showing how many periodic numbers are in the interval from $l$ to $r$ (both ends are included).

In the first sample periodic numbers are $3$ , $7$ and $10$ .

In the second sample periodic numbers are $31$ and $36$ .