System of Equations 2

Limits: 2 sec., 256 MiB

You are given two non-negative integers \(a\) and \(b\).

Find the number of triples of non-negative integers \((x, y, z)\) such that

• \(x+y+z=a\)

• \(x \mbox{ XOR } y \mbox{ XOR } z = b\).

Input

The single line of the input contains two integers \(a\) and \(b\).

Output

Print the only integer — answer to the problem.

Constraints

\(0 \le a, b \le 10^9\).

Samples

Input (stdin) сopy	Output (stdout) сopy
74 44	27

Input (stdin) сopy	Output (stdout) сopy
4 7	0

Notes

Triples \((x_1, y_1, z_1)\) and \((x_2, y_2, z_2)\) are considered distinct if \(x_1 \ne x_2\) or \(y_1 \ne y_2\) or \(z_1 \ne z_2\).