Problem Description

If the binary representation of a positive integer has each bit (either $0$ or $1$) with at least one identical bit to its left or right, Dr. X considers it a "lucky number." For example:

• $(1)_2 = (1)_{10}$ has a lone $1$, so it is not a lucky number.
• $(110111)_2 = (55)_{10}$ has a lone $0$, so it is not a lucky number.
• $(111110011)_2 = (499)_{10}$ is a lucky number.
• $(110011001100)_2 = (3276)_{10}$ is a lucky number.

For given integers $a$ and $b$, Dr. X wants you to find the number of lucky numbers in the range $a, a + 1, a + 2, \dots, b$.

Input Format

Input consists of two space-separated integers $a$ and $b$.

Output Format

Output a single integer representing the number of lucky numbers between $a$ and $b$.

Sample Input and Output

Sample Input #1

1 100

Sample Output #1

14

Sample Input #2

4096 65535

Sample Output #2

1364

Notes

For $100\%$ of the data, it is guaranteed that $1 \leq a \leq b \leq 10^6$.

The original full score for this problem was $15\text{pts}$.

见题面 Input 部分

见题面 Output 部分