XOR Equation
题目描述
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≤1012, 0≤x≤1012), 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).
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