Solve this interesting problem

Time Limit: 2000/1000 MS (Java/Others)

Memory Limit: 32768/32768 K (Java/Others)

Description

Have you learned something about segment tree? If not, don’t worry, I will explain it for you.
Segment Tree is a kind of binary tree, it can be defined as this:
- For each node u in Segment Tree, u has two values: $L_u$ and $R_u$.
- If $L_u = R_u$, u is a leaf node.
- If $L_u \neq R_u$, u has two children x and y,with $L_x = L_u$,$R_x = \lfloor \frac{L_u + R_u }{2}\rfloor$,$L_y = \lfloor \frac{L_u + R_u }{2}\rfloor + 1$,$R_y = R_u$.
Here is an example of segment tree to do range query of sum.



Given two integers L and R, Your task is to find the minimum non-negative n satisfy that: A Segment Tree with root node's value $L_{root} = 0$ and $R_{root} = n$ contains a node u with $L_u = L$ and $R_u = R$.

Input

The input consists of several test cases.
Each test case contains two integers L and R, as described above.
$0 \leq L \leq R \leq 10^9$
$\frac{L}{R-L+1} \leq 2015$

Output

For each test, output one line contains one integer. If there is no such n, just output -1.

Sample Input

6 7 10 13 10 11

Sample Output

7 -1 12

Hint

wange2014

Source

2015 Multi-University Training Contest 3

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