I. Two's a Team
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

$$$Abodeh$$$, $$$Nowar$$$, and $$$Hussein$$$ decided to organize a football tournament. In each match, exactly $$$2$$$ players are required to play. For any village with $$$x$$$ people, they want to know how many full matches they can organize, leaving at most one person as a substitute. Let this number be $$$f(x)$$$.

Now, they are given a range of villages from $$$L$$$ to $$$R$$$. They need your help to calculate the total number of matches they can organize across all these villages.

More formally:

$$$f(x)$$$ is the number of terms equal to $$$2$$$ in the representation of $$$x$$$ as a sum of several $$$2$$$'s and, if needed, one $$$1$$$.

For example:

  • $$$5 = 2 + 2 + 1 \rightarrow f(5) = 2$$$.
  • $$$6 = 2 + 2 + 2 \rightarrow f(6) = 3$$$.
  • $$$7 = 2 + 2 + 2 + 1 \rightarrow f(7) = 3$$$.

You need the sum of $$$f(x)$$$ for all $$$x$$$ from $$$L$$$ to $$$R$$$:

$$$$$$ Answer = \sum_{x=L}^{R} f(x). $$$$$$

Input

The only line of input contains two integers $$$L$$$ and $$$R$$$ ($$$1 \le L \le R \le 10^5$$$).

Output

Print a single integer — the required sum.

Examples
Input
2 9
Output
20
Input
51 501
Output
62125
Input
2 56
Output
784
Input
4 5
Output
4
Input
4 15
Output
54