Solve this interesting problem

Problem 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

Author

ZSTU

Source

2015 Multi-University Training Contest 3