POWFIB  Fibo and non fibo
The problem is simple.
Find (a^b) % MOD
where ,
a = Nth nonfibonacci number
b = (Nth fibonacci number)%MOD
MOD = 10^9+7
Consider fibonacci series as 1,1,2,3,....
Note : It is guaranteed that Nth nonfibonacci number will always be less than MOD value for every value of N used.
Input
First line contains T , the number of test cases.
Each next T lines contains a number N.
Output
Print T lines of output where each line corresponds to the required answer.
Announcement: Constraints are updated. Sorry for inconvenience occurred.
Example
Input:
3 3 2 1
Output:
49 6 4
Explanation
For N=3 : 3rd non fibo number =7, 3rd fibo number=2. ans= (7^2) %MOD =49
For N=2 : 2nd non fibo number =6, 2nd fibo number=1. ans=(6^1) %MOD=6
For N=1 : 1st non fibo number =4, 1st fibo number=1. ans= (4^1) %MOD =4
Constraints
1<=T<=100000
1<=N<=9*10^8
Note: Test cases have been updated and costraints are changed. Those who get TLE or WA are suggested to resubmit. GOOD LUCK there.
hide comments
[Lakshman]:
20150719 12:47:40
@Mohib Your solution is no more faster, see the updated list. Best is .17s


:.Mohib.::
20150719 08:19:31
@Lakshman awesome speed!! Congratulations...!! Last edit: 20150719 20:50:18 

[Lakshman]:
20150718 18:01:09
@All problem is ready http://www.spoj.com/problems/POWFIB2/


Kata:
20150718 15:01:19
@luckymastermin :


[Lakshman]:
20150718 14:19:20
@wisfaq I mean with hard constraints we can get more elegant solution.


hrishabh:
20150718 11:47:10
Finally!!


wisfaq:
20150717 21:44:16
@Lakshman:


[Lakshman]:
20150717 15:16:26
As this seems to easy we can create another version of this with higher constraints with n <=1e16 ~ 1e18 what other thinks. 

eightnoteight:
20150716 19:48:59
nice one!


:?ToRpiDo:
20150716 18:57:10
@ivar.raknahs : Can you plz check my submission, I think my algorithm is correct. :(

Added by:  ivar.raknahs 
Date:  20150715 
Time limit:  1s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ASM64 JSMONKEY 
Resource:  OWN 