Problem2096--XOR Equation

2096: XOR Equation

Time Limit: 2 Sec  Memory Limit: 256 MB
Submit: 0  Solved: 0
[Submit] [Status] [Web Board] [Creator:]

Description

time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

Two 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).

Source/Category