Good Numbers

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A number is called a square free number if there does not exist a number greater than 1, whose square divides the number evenly/perfectly. For example, number 8 is not a square free number as number 4 (which is square of 2), divides 8. Similarly, number 4 is also not a square free number. However numbers 1, 3, 6 all are square free numbers.
A number n is called a good number if following properties hold.
 It is a square free number.
 Let s denote the sum of all divisors of n (including nontrivial divisors like 1 and itself). Let c denote the number of prime numbers dividing s. Number c should be a prime number.
You will two numbers L, R, you have to find sum of divisors (including nontrivial) of all the good numbers in the range L to R, both inclusive.
Please note that 0 is not considered a prime number.
Input
The first line of the input contains an integer T denoting the number of test cases. The description of T test cases follows.
The only line of the each test case contains two space separated integers L, R denoting the range for which you have to find sum of divisors of good numbers.
Output
For each test case, output a single line corresponding to answer of the test case.
Constraints and Subtasks
Subtask #1 (30 points)
 1 ≤ T ≤ 10^{3}
 1 ≤ L ≤ R ≤ 10^{3}
Subtask #2 (70 points)
 1 ≤ T ≤ 10^{5}
 1 ≤ L ≤ R ≤ 10^{5}
Example
Input 2 1 5 6 10 Output: 6 30
Explanation
 Following number in the range 1 to 10 are square free numbers : 1, 2, 3, 5, 6, 7, 10.
 Sum of their divisors will be 1, 3, 4, 6, 12, 8, 18 respectively.
 Number of prime divisors of their sum of divisors will be 0, 1, 1, 2, 2, 1, 2 respectively.
 So, the number 5, 6, 10 are good numbers.
Example case 1. Only good number in 1 to 5 is 5. Sum of divisors of 5 is 6.
Example case 2. In the range 6 to 10, number 6 and 10 are good. Sum of their divisors is 12 + 18 = 30.
Author:  admin2 
Tags  admin2 
Date Added:  23062016 
Time Limit:  1 sec 
Source Limit:  50000 Bytes 
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