Total number of Equal Partition
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  Difficulty: Medium   Marks: 4

For a number  f(N) = the total number of parts in the partitions of N into equal parts.
 

For example
if the given number is 4, the equal partitions will be:

{1,1,1,1}   ->total parts=4

{2,2}        -> total parts=2

{4}           -> total parts=1

So,  the total number of parts in the partition of 4 into equal parts is 7.

Now you are given two number l,r. find the sum of f(i) for i=l to r.(both inclusive)
 

Input:

First line of input contains a single integer T denoting the number of test cases.

Each line of test case containing two space separated integers l and r as described in the problem statement.


Output:

For each test case, output a single integer containing the sum as described in the problem statement.


Constraints:

1<=T<=100

1<=l<=r<=10^7


Example:

Input
1
1 2

Output

4

** For More Input/Output Examples Use 'Expected Output' option **

Contributor: Pranay Pandey
Author: pra1nay7_313


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