Statement

Timothy is a young computer scientist who has recently been exploring the fascinating properties of binary arithmetic. While organizing some old manuscripts left by his grandfather, he stumbled upon a mysterious mathematical formula:

$$(x \ \&\ y) + (x \ |\ y) = T$$

Here, $T$ represents the "balanced number", and the bitwise operators $\&$ and $|$ represent bitwise AND and bitwise OR operations, respectively. In mainstream programming languages, & is used to represent bitwise AND, for example, int c = a \& b is represented as $c\leftarrow a\ \&\ b$, and bitwise OR is similarly represented.

To be precise, the bitwise AND operator follows this rule: the result bit is 1 only when both corresponding binary bits are 1; otherwise, it is 0. For example, consider calculating $5\ \&\ 9$ (the lower right corner indicates the base 10 or base 2)

$$5_{(10)}\ \&\ 9_{(10)} = 0101_{(2)}\ \&\ 1001_{(2)}=0001_{(2)}=1_{(10)} $$

Similarly, bitwise OR means that when at least one of the two corresponding bits is 1, the result bit is 1; otherwise, it is 0.

Timothy speculated that this formula might hide some kind of symmetry in binary bit operations. If he could find the smallest positive integer $y$ that satisfies the condition, he would be able to unlock the next password in the notebook.

However, not all pairs of $x$ and $T$ can find a corresponding $y$. If no such $y$ exists, it indicates that this $x$ has no affinity with the "balanced number", and a return value of $-1$ is required.

Please help Timothy write a program to find the smallest positive integer $y$ for a given $x$ and $T$, or determine if it does not exist.

Input

The input contains a line with two integer numbers representing $x$ and $T$ respectively, where $(0 \leqslant x,T \leqslant 1 \times 10^{18})$ and they are separated by a space.

Output

It contains an integer representing $y$.

Samples

114514 1919810

1805296

1919810 114514

-1