Let $\text{ctz}(x)$ be the number of trailing zeros in the binary representation of $x$, for example, $\text{ctz}(1001000_2)=3$.

Let $\text{ppc}(x)$ be the number of ones in the binary representation of $x$, for example, $\text{ppc}(1001000_2)=2$.

A number is defined as a "good number" if and only if $\text{ctz}(x)=\text{ppc}(x)$.

Given $Q$, there are $Q$ queries. Each query provides an interval $[l,r]$, and you need to find any good number in $[l,r]$, or determine that no such number exists.

Input

The first line contains a positive integer $Q$.

Each of the next $Q$ lines contains two positive integers $l$ and $r$.

Output

For each query, output one line. If there exists a good number in the interval $[l,r]$, output any such good number; otherwise, output $-1$.

Examples

Input 1

5
38 47
57 86
23 24
72 83
32 33

Output 1

-1
68
-1
-1
-1

Input 2

See the provided files.

Output 2

See the provided files.

Constraints

This problem uses bundled subtasks.

For all data, it is guaranteed that $1\le Q\le 10^5$ and $1\le l\le r\le 10^9$.