KPOWERSUM  Kth Power Summation
Leeana Learned Few New Things Few Days Ago , Like:
1) Find The Summation Of Divisors.
2) Modular Arithmetic
So Now Her Uncle Gave Her A Task.
Task Is: You Will Be Given A Number(N) And Another Number(K). Now You Have To Find K_{th} Power Summation Of Divisors Of N.
Summation Of All Divisors Of N Will Be Huge, So You Have To Print The Summation Module (M=1000000007).
Like: Divisors Of 6 is: ( 1 2 3 6 ) And K = 2.
so, summation is: 1^K+2^K+3^K+6^K = 1^2 + 2^2 + 3^2 + 6^2= 1+4+9+36 = 50%1000000007=50
Leeana Thinks That You Are A Great Programmer, So She Needs Your Help. Can You Help Her??? :D :D :D
Input
Input Starts With An Integer T (≤ 500), Denoting The Number Of Test Cases. Each Case Contains An Integer N (1 ≤ N ≤ 10^{15}) And An Integer K (1 ≤ K ≤ 10^{5}) Denoting The Power Of Divisors.
Output
For Each Test Cases, Print The Case Number And The Kth Power Summation Of Divisors Of N Module 1000000007. After Each Case Print A New Line. See Sample Input And Output For Better Explanation.
Example
Input: 4 6 2 6 1 6 4 6 3
Output: Case 1: 50 Case 2: 12 Case 3: 1394 Case 4: 252
#Extra_Challenge: N<=10^18, T<=1000 TL: 1s
hide comments
Scape:
20200406 15:37:21
Fix the sample output and the description. You need to print two new lines after printing the sample output. Something like printf("Case %d: %d\n\n", case_no, ans);


rayhan50001:
20191029 11:50:41
TEST CASE UPDATED. :(


prodipdatta7:
20191019 10:18:28
Week dataset :


joydas0111:
20180920 18:12:10
getting TLE


[Lakshman]:
20180916 20:05:15
@problem setter, Even if you set a new problem with new constraints which you have mentioned (Extra_Challenge: N<=10^18, T<=1000 TL: 1s) will not be enough, If you are still interested in setting a challenge make T <=5000 or 10000


julkas:
20180916 13:32:24
@rayhan50001 Where is Extra_Challenge problem with new constraints?


shubham_001:
20180906 20:02:08
Giving TLE , can you tell expected time complexity? 

bdezso:
20180906 07:48:08
Could you check my last submission? :/ TLE with formula.


[Lakshman]:
20180905 11:28:26
Not sure why I am getting wrong answer now. @RaYHan may I have a test case where my new code is failing.


Kata:
20180905 10:54:51
Did you fixed the test cases for judge, not just the sample? I do not think my code was wrong.

Added by:  RaYHan 
Date:  20180902 
Time limit:  1s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All 
Resource:  Own Problem 