LOCKER  Magic of the locker
Vertu, the clever businessman, sells the ropes to his customers at the rate of 1 rupee per meter. He can only sell an integer length of a rope to a customer. Also, he has a magic locker which functions this way:
Suppose the locker has 'x' rupees. Now if 'y' rupees more are put into this locker, it multiplies them and total money in the locker now is 'x*y'.
This morning, Vertu starts his bussiness with 'n' meters of rope. He puts 1 rupee in the locker as to have good luck.
Find the maximum money he can earn today considering that he sold all of his rope at the end of the day.
NOTE: Vertu has to put all rupees into the locker as soon as he gets it, and can get rupees from locker only at the end of the day.
Input and Output
The first line contains t, the number of test cases. t lines follow, each containing one positive integer n. For each of these integers, print the required answer modulo(10^{9}+7).
Constraints
t<10^{5}
0<n<10^{12}
Example
Input:
2
4
5
Output:
4
6
hide comments
hemlocktree:
20231007 04:08:25
In simple words, you are given a number n , and break it into parts such that product of all parts is maximum. 

sachin_08:
20220323 18:50:07
Hint : Month of the question added ! 

srinivas_499:
20210930 14:50:10
tle in c++


rachitatrey23:
20210510 14:22:20
can anyone please check my solution n I am getting WA id>27861418 

sabbir0152:
20200703 09:12:47
incomplete problem ... 

heisunbug:
20200605 11:24:35
Also take care of base case 

shuhbo:
20200513 19:41:36
Don't really understand. Python gives me TLE, but c++ gives me accepted. 

anurag_mishra:
20200425 03:19:24
modular exponentiation... AC


whoopwhoop:
20200416 10:51:45
@lalitkundu please tell why am i getting a wa my submission id is 25779593


ajay_panchal:
20200327 08:34:03
test case ? 
Added by:  darkshadows 
Date:  20130328 
Time limit:  1s 
Source limit:  5000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ASM64 
Resource:  Own problem 