Problem Statement

You are given positive integers $L$ and $R$ satisfying $L\le R$.

A sequence of positive integers $A=(A_L,A_{L+1},\ldots,A_R)$ of length $R-L+1$ satisfying the following condition is called a good integer sequence:

• For every pair of integers $(i,j)$ satisfying $L\le i < j\le R$, if $A_i = A_j$, then $\operatorname{popcount}(i)<\operatorname{popcount}(j)$.

Find the minimum value of $\max(A_L,A_{L+1},\ldots,A_R)$ over all good integer sequences $A=(A_L,A_{L+1},\ldots,A_R)$.

You are given $T$ test cases; solve each of them.

What is $\operatorname{popcount}$? For a non-negative integer $x$, $\operatorname{popcount}(x)$ is the number of $1$'s when $x$ is written in binary. More precisely, when a non-negative integer $x$ satisfies $\displaystyle x=\sum _ {i=0} ^ \infty b _ i2 ^ i\ (b _ i\in\lbrace0,1\rbrace)$, $\displaystyle\operatorname{popcount}(x)=\sum _ {i=0} ^ \infty b _ i$.

For example, $13$ written in binary is 1101, so $\operatorname{popcount}(13)=3$.

Constraints

• $1\le T\le 10^4$
• $1\le L \le R\le 10^{18}$
• All input values are integers.

Input

The input is given from Standard Input in the following format:

• $T$
• $\text{case}_1$
• $\text{case}_2$
• $\vdots$
• $\text{case}_T$

Each test case is given in the following format.

• $L$ $R$

Output

Output $T$ lines.

The $i$-th line $(1\le i\le T)$ should contain the answer for the $i$-th test case $\text{case}_i$.

5
3 6
1 1
2 15
100 10000000
514284786278117031 620546740167642909

3
1
6
1636985
11375123021856567

Consider the first test case.

$(A_3,A_4,A_5,A_6)=(1,2,2,3)$ is a good integer sequence, and $\max(A_3,A_4,A_5,A_6)=3$.

There is no good integer sequence with $\max(A_3,A_4,A_5,A_6) < 3$, so output $3$ on the first line.

• Source: AtCoder ABC 476 G