XOR Equation

Interview

Time limit2sMemory limit512 MB

Summary

Count ordered pairs of positive integers A and B with A+B=S and A xor B=X.

Level: Medium6 of 10
Topics: Math, Bit manipulation
Solved: No attempts yet

Problem

You are given two positive integers $S$ and $X$ . Count the ordered pairs $(A, B)$ of positive integers that satisfy $A + B = S$ and $A \oplus B = X$ , where $\oplus$ is the bitwise exclusive or.

Both $A$ and $B$ must be at least $1$ . If $A \neq B$ , then $(A, B)$ and $(B, A)$ count as two different pairs.

Input

The first line contains two positive integers $S$ and $X$ , separated by a space. ( $2 \le S, X \le 10^{12}$ )

Output

Print on the first line the number of ordered pairs $(A, B)$ that satisfy both equations.

Examples3

Example 1
Input
```
9 5
```
Expected output
```
4
```
Example 2
Input
```
3 3
```
Expected output
```
2
```
Example 3
Input
```
5 2
```
Expected output
```
0
```