Define F(n,k) = Sum of kth powers of all divisors of n
So for example F(6,2) = 1^2 + 2^2 + 3^2 + 6^2 = 50

Define further G(a,b,k) as : Sum of F(j,k) where j varies from a to b both inclusive

Your task is to find G(a,b,k) given a,b & k.
As values of G can get very large , you only need to output the value of G(a,b,k) modulo 10^9+7.

Input Format:

First line of input file contains a single integer T - denoting the number of test cases.
The follow description of T test cases. Each test case occupies exactly one line which contains three space separated integers a,b & k.

Output Format:

Output your result for each test case in a new line.

Sample Input File:

2
2 2 1
1 3 2

Sample Output File:

3
16


Description of sample output:

In case 1, we are to find sum of divisors of 2. which is nothing but 1+2=3.
In case 2, we are to find sum of squares of divisors of 1 2 & 3. So for 1 sum is = 1. For 2 sum is = 1^2+ 2^2= 5. For 3 sum is = 1^2 + 3^2=10.
So ans is 16.

Constraints :

1<=a<=b<=10^5
1<=k<=10^5
Number of test cases <=20