Number of pairs

Limits: 2 sec., 256 MiB

This statement was translated automatically from Ukrainian.

Zenyk became interested in how many pairs of integers \((a, b)\) exist such that

• \(l \le a \le b \le r\),

• \(a + b = a \mbox{ XOR } b\).

Help Zenyk — calculate the answer for him.

Input

The single line contains two integers \(l\) and \(r\).

Output

In the single line, print an integer — the answer to the problem.

Constraints

\(0 \le l \le r \le 10^9\).

Samples

Input (stdin) сopy	Output (stdout) сopy
2 5	3

Notes

Pairs satisfying the condition in the example: (2, 4), (2, 5), (3, 4).