627A.XOR Equation

A. XOR Equation

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).

先贴我未通过的程序

[python] view plain copy

 

1. #!/usr/bin/python  
2. #-*-coding:utf-8 -*-  
3. s,x=map(int,raw_input().split(' '))  
4. count=0  
5. if s>x or s<3:  
6.     if s%2==0:  
7.         n=s/2+1  
8.     else:  
9.         n=(s+1)/2  
10.     for i in range(1,n):  
11.         a=i  
12.         b=s-i  
13.         if a^b==x:  
14.             count=count+2  
15.             if a==b:  
16.                 count=count-1  
17. elif s==x:  
18.     count=s-1  
19. elif x>s:  
20.     count=0  
21. print count  

Runtime error

[python] view plain copy

 

1. def solve(s, x):  
2.     d = (s - x)  
3.     if x << 1 & d or d%2 or d<0: return 0  
4.     return 2 ** (bin(x).count('1')) - (0 if d else 2)  
5. s, x = map(int, raw_input().split(' '))  
6. print(solve(s, x))  

当x左移1位与d==1或者d%2==1或s<x时，直接返回0

否则返回2**(bin(x).count('1'))-(0 if d else 2)

数学问题吧