FIBOSUM - Fibonacci Sum

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The fibonacci sequence is defined by the following relation:

  • F(0) = 0
  • F(1) = 1
  • F(N) = F(N - 1) + F(N - 2), N >= 2

Your task is very simple. Given two non-negative integers N and M, you have to calculate the sum (F(N) + F(N + 1) + ... + F(M)) mod 1000000007.

Input

The first line contains an integer T (the number of test cases). Then, T lines follow. Each test case consists of a single line with two non-negative integers N and M.

Output

For each test case you have to output a single line containing the answer for the task.

Example

Input:
3
0 3
3 5
10 19

Output:
4
10
10857

Constraints

  • T <= 1000
  • 0 <= N <= M <= 109

hide comments
Alexandre Henrique Afonso Campos: 2013-11-11 23:39:41

I have a solution that works for all listed cases here and in the forums previously mentioned here in the comments, including trick cases. Still getting WA.

Edit:
AC after considering the case that m>n but f(m)%1000000007 < f(n)%1000000007.

Last edit: 2013-11-11 23:49:45
Rafael Perrella: 2013-09-11 22:43:50

I don't know any link where it is discussed. But you can start a thread and post the link here, then we can discuss it there.

@edit
I created the thread. You can easily find it in the forum.

Last edit: 2013-09-12 04:13:41
Ouditchya Sinha: 2013-09-11 15:50:43

@Rafael Perrella : Thank you for answering my question & congratulations for solving this problem in 0.00s. :)

Yes, I solved this using matrix exponentiation. O(__builtin_popcount(N)) is definitely better than O( log(N) ). Can you please provide any link where this type of algorithm is discussed? Or maybe we can start a thread on forum?

@Rafael Perrella : Thank You for sharing your Algorithm!! I'll try to understand it. :)

Last edit: 2013-09-12 12:09:37
Rafael Perrella: 2013-09-11 12:05:03

@Mayank 999975531
@Ouditchya Did you calculate F(N) using matrix exponentiation? It's not fast enough to get 0.00, I guess. My algorithm, for a given N, calculates F(N) in O(__builtin_popcount(N)) time, with a really small constant. I wrote this algorithm based on the following property:
F(n+k) = F(k)F(n+1) + F(k-1)F(n)

YoungMoon KO: 2013-09-07 04:37:52

Excellent problem. I've learned a lot of things about Fibonacci sequence.
Refers http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibFormula.html#exact

Last edit: 2013-09-07 04:38:51
hiddenman: 2013-09-06 20:40:18

gud 1
learn a lot abt fibo series....... :)

Ouditchya Sinha: 2013-08-26 20:04:43

How is 0.00s possible? I can only get 0.01s.

Anubhav Balodhi : 2013-08-25 09:33:06

got ac in 3rd try, learnt a lot about fibonacci numbers :D

Amitayush Thakur: 2013-08-19 13:06:10

good question to learn application of Divide and conquer :)

: 2013-07-11 21:50:19

learned something new :D


Added by:David Gómez
Date:2010-12-04
Time limit:1s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ASM64
Resource:My Own