Cherry isn't feeling well right now as she found a problem that she couldn't solve. So she started to listen to On the Sea and you, to make her happy, have to solve the problem for her.
For any non-negative integer $n$
, let $f(n)$
be the median of the submasks of $n$
.
You are given two integers $l$
and $r$
. You have to find the median of the sequence $f(l), f(l + 1), \ldots, f(r)$
.
An integer $x$
is a submask of $y$
if $x$
can be obtained by replacing some (possibly none or all) $1$
-s in the binary representation of $y$
by $0$
-s.
The median of a sequence is the value of an element which is in the middle of the sequence after sorting it in non-decreasing order. If the length of the sequence is even, the left of two middle elements is used. For example, the median of $[4,2,7,5]$
is $4$
since after sorting the sequence, it will look like $[2,4,5,7]$
and the left of two middle elements is equal to $4$
. The median of $[7,1,2,9,6]$
equals $6$
since after sorting, the value $6$
will be in the middle of the sequence.
The first line of the input contains a single integer $t(1 \le t \le 10^5)$
denoting the number of test cases. The description of $t$
test cases follows.
The first and only line of each test case contains two space-separated integers $l$
and $r$
$(1 \le l \le r \le 10^9)$
.
For each test case, print a single line containing the median of the of the sequence $f(l), f(l + 1), \ldots, f(r)$
.
Input | Output |
---|---|
3 1 5 7 10 696969 69696969 | 0 1 8073418 |
In the second test case, The sorted list of the submasks of So we have to find the median of the sequence |