Josuke and Complete Graph
Description
Josuke received a huge undirected weighted complete$^\dagger$ graph $G$ as a gift from his grandfather. The graph contains $10^{18}$ vertices. The peculiarity of the gift is that the weight of the edge between the different vertices $u$ and $v$ is equal to $\gcd(u, v)^\ddagger$. Josuke decided to experiment and make a new graph $G'$. To do this, he chooses two integers $l \le r$ and deletes all vertices except such vertices $v$ that $l \le v \le r$, and also deletes all the edges except between the remaining vertices.
Now Josuke is wondering how many different weights are there in $G'$. Since their count turned out to be huge, he asks for your help.
$^\dagger$ A complete graph is a simple undirected graph in which every pair of distinct vertices is adjacent.
$^\ddagger$ $\gcd(x, y)$ denotes the greatest common divisor (GCD) of the numbers $x$ and $y$.
The first line contains one integer $t$ ($1 \le t \le 100$) — the number of test cases.
The first line of each test case contains two numbers $l$, $r$ ($1 \le l \le r \le 10^{18}$, $l \le 10^9$).
For each test case print a single number — the number of different weights among the remaining edges.
Input
The first line contains one integer $t$ ($1 \le t \le 100$) — the number of test cases.
The first line of each test case contains two numbers $l$, $r$ ($1 \le l \le r \le 10^{18}$, $l \le 10^9$).
Output
For each test case print a single number — the number of different weights among the remaining edges.
7
2 4
16 24
2 6
1 10
3 3
2562 2568
125 100090
2
6
3
5
0
5
50045
Note
The graph $G'$ for the first test case. The picture above shows that the graph has $2$ different weights.
In the fifth test case, there is only one vertex from which no edges originate, so the answer is $0$.