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
priyasatbhaya: 2016-09-09 02:42:29

@baadshah_ thanks for the negative modulus solution

lakshay_v06: 2016-08-16 22:19:13

In case of a doubt, check out the resources mentioned here : http://programmerheaven9.blogspot.in/2011/10/spoj-fibosum.html

swap: 2016-07-31 07:26:43

Learnt a lot! @baadshah_ thanks! It took me some time to understand about negative modulus!

sonali9696: 2016-07-17 20:48:07

Oh god the mod..! Cost me 9 WAs! You don't have to apply mod to just the answer. You have to apply mod to the matrix at each single step(each time you multiply matrices)!! No idea why even after using long long int!!

baadshah_: 2016-07-15 20:57:01

if u get negative ans just add 1000000007 to the ans!!

harsh gupta: 2016-06-11 22:40:31

can anyone post a tricky test case which involves negative modulo ??

lynx_: 2016-05-24 11:50:04

Used Dijkstra's formula...with memorization...
F(2*n-1)=F(n)*F(n)+F(n-1)*F(n-1)
F(2*n)=(2*F(n-1)+F(n))*F(n)..
0.02 secs..AC

piyushhh: 2016-05-21 16:25:12

I mistakingly printed 1 for 0 0 case . -_- . costed me 3 WA!!

SUBHAM SANGHAI: 2016-05-13 11:02:39

@buttman , Though given n<=m .But you are taking mod with 10^9+7;So there might be a problem of a negative mod.Take this case ,suppose (N!)=(10^9+6) and (M)!=(10^9)+8, (M!)%mod=1 and (N!)%mod=(10^9)+6;
so here (M!)-(N!) <0

Last edit: 2016-05-13 11:05:05
buttman: 2016-05-09 11:18:54

Last edit: 2016-05-14 05:32:30

Added by:David Gómez
Date:2010-12-04
Time limit:0.838s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All
Resource:My Own