SP7567 IITD4 - Divisor Summation Powered

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

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