## POWFIB - Fibo and non fibo

The problem is simple.

Find  (a^b) % MOD

where ,

a = Nth non-fibonacci number

b = (Nth fibonacci number)%MOD

MOD = 10^9+7

Consider fibonacci series as 1,1,2,3,....

Note : It is guaranteed that Nth non-fibonacci 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.

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.`

 < Previous 1 2 3 4 5 Next > Soma: 2015-07-15 19:20:03 @anyone : is a>0 or a>=0 ? --(ans)-- a>0 Last edit: 2015-07-15 19:20:46 Kata: 2015-07-15 18:49:15 @luckymastermin : This problem ask to calculate (non_fib ^ (fib % mod)) % mod, not (non_fib ^ fib) % mod [Lakshman]: 2015-07-15 18:27:36 @ivar.raknahs I think the entire INPUT file is wrong you check my code AC one and wrong answer. NOTE:: how come you are calculating non Fibonacci ^ Fibonacci on same mod which is 1000000007. here we need to apply Euler's theorem in order to solve this. But as I checked your input file based on mod 1000000007 only. -reply-> you need to calculate (a^ (b % mod ) ) % mod not (a^b)%mod and please read the note statement. I hope this helps. Last edit: 2015-07-16 05:23:57 Abhishek Guha: 2015-07-15 18:05:00 I am getting WA :( @mohib, can you check my code ? :.Mohib.:: 2015-07-15 17:47:10 Assuming n<=10^7 and t<=10^5. I got AC :) [Lakshman]: 2015-07-15 17:33:10 Please mention the upper and lower bound for n. Can you check my submission, I think my algorithm is correct. :.Mohib.:: 2015-07-15 14:07:47 What is the bounds for n and t?? -reply-> constraints updated Last edit: 2015-07-16 05:04:49