System of Equations

Limits: 2 sec., 256 MiB

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

Find any non-negative integers \(x\), \(y\), \(z\) such that

• \(x+y+z=a\)

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

or report that they don’t exist.

Input

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

Output

If there exist non-negative integers \(x\), \(y\), \(z\) which satisfy the condition print any such triple.

Otherwise print the only integer -1.

Constraints

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

Samples

Input (stdin) сopy	Output (stdout) сopy
74 44	15 13 46

Input (stdin) сopy	Output (stdout) сopy
4 7	-1

Notes

\(15+13+46=74\),

\(15 \mbox{ XOR } 13 \mbox{ XOR } 46 = {1111}_2 \mbox{ XOR } {1101}_2 \mbox{ XOR } {101110}_2 = {101100}_2 = 44\).