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: Lu and Ru.

- If Lu=Ru, u is a leaf node.

- If Lu≠Ru, u has two children x and y,with Lx=Lu,Rx=⌊Lu+Ru2⌋,Ly=⌊Lu+Ru2⌋+1,Ry=Ru.

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 Lroot=0 and Rroot=n contains a node u with Lu=L and Ru=R.

Input:

The input consists of several test cases.

Each test case contains two integers L and R, as described above.

0≤L≤R≤109

L/(R−L+1)≤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

Source:

Submit