IITD4 - Divisor Summation Powered

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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

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

 < Previous 1 2 Next > rishabh_1997: 2016-07-10 12:07:53 Learnt some new things, use modular exponentiation for faster power calculation AC 2.03s in third attempt , after 2 TLEs. A much recommended problem. newbie: 2015-11-14 20:57:43 easy one just simple logic is enough :) Malinga: 2015-01-15 07:35:44 consider ** times=b/i - (a-1)/i ** caused me two WA.. Yashpal: 2014-12-30 08:36:52 O(sqrt(b)+sqrt(a))logn giving AC in 15 Sec .. :( Any sort of Optimization ?? Last edit: 2014-12-30 08:37:09 Bharath Reddy: 2014-09-29 16:05:00 Got AC with a generic implementation. No need of code optimizations. A good algorithm is enough Hint: Look at the constraints closely :) Last edit: 2014-09-29 16:11:46 oye lakshman help plz: 2014-06-29 03:04:54 @lakshman is this the correct ans 299384888 also is there any fast algo for powersum here is my code https://ideone.com/mz3gZn kindly help me Last edit: 2014-06-29 03:06:12 [Lakshman]: 2014-06-29 02:59:39 @crazzysuarez Have you tried this case 1 1 100000 9999 Last edit: 2014-06-29 03:02:14 tyson: 2014-06-28 20:42:41 getting WA plz provide with some test case @nikhil sub id 11848600 Rishav Goyal: 2014-04-20 09:46:59 yay :DDDDDD finalyy AAAcCCCCC :) Prakhar Gupta: 2014-01-22 14:51:06 nlog(n) always giving TLE on running (10) Last edit: 2014-02-23 14:08:36