FIBOSUMT  Fibonacci extraction Sum
Some people may found FIBOSUM a too easy problem. We propose here a useful variation.
Fib is the Fibonacci sequence:
For any positive integer i: if i<2 Fib(i) = i, else Fib(i) = Fib(i1) + Fib(i2)
Input
The first line of input contains an integer
T, the number of test cases.
On each of the next T lines, your are given
tree integers c, k, N.
Output
Print Sum(Fib(ki+c) for i in [1..N]).
As the answer could not fit in a 64bit container, just output your answer modulo 1000000007.
Example
Input: 1 3 5 2
Output: 254
Explanations
Index1 Fib sequence : 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, ...
We want the 5*1+3 = 8^{th} and 5*2+3 = 13^{th} ones, thus the answer is 21 + 233 = 254.
Constraints
0 < T <= 60606 0 <= c < k <= 2^15 0 < N <= 10^18
The numbers c,k,N are uniform randomly chosen in their range.
For your information, constraints allow 1.3kB of Python3 code to get AC in 0.30s, it could be hard.
A fast Ccode can get AC around 0.01s. (Timing edited 20170211, after compiler changes)
Warning: Here is Cube cluster, you can try the classical edition (clone with Pyramid cluster).
Have fun ;)
hide comments
aniket_1729:
20150806 11:52:57
could k*n+c >10^18?


[Lakshman]:
20140517 16:53:02
@Francky any suggestion why I am getting WA. Thanks.


(Tjandra Satria Gunawan)(æ›¾æ¯…æ˜†):
20140408 21:59:48
Thank you for tutorial edition :) 
Added by:  Francky 
Date:  20140406 
Time limit:  10s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ASM64 
Resource:  Own Problem 