8VC Venture Cup 2016 - Final Round |
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math

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A. XOR Equation

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputTwo positive integers *a* and *b* have a sum of *s* and a bitwise XOR of *x*. How many possible values are there for the ordered pair (*a*, *b*)?

Input

The first line of the input contains two integers *s* and *x* (2 ≤ *s* ≤ 10^{12}, 0 ≤ *x* ≤ 10^{12}), the sum and bitwise xor of the pair of positive integers, respectively.

Output

Print a single integer, the number of solutions to the given conditions. If no solutions exist, print 0.

Examples

Input

9 5

Output

4

Input

3 3

Output

2

Input

5 2

Output

0

Note

In the first sample, we have the following solutions: (2, 7), (3, 6), (6, 3), (7, 2).

In the second sample, the only solutions are (1, 2) and (2, 1).

Codeforces (c) Copyright 2010-2023 Mike Mirzayanov

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