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
xom__b: 2019-10-26 11:03:38

use (a%mod -b%mod +mod)%mod) instead of (a-b)%mod

importme: 2019-09-25 20:42:35

The case of negative modulos is interesting....

violet360: 2019-09-17 18:58:23

normal iteration won't work, will obviously give TLE
use matrix exponentiation(O(log(n))
and use modulo cleverly, good luck :)

Last edit: 2019-09-17 18:59:07
prashantpx_1: 2019-07-21 21:34:22

Take Care of Data Type...! Got 2 WA for using int and long int.

ramini1996: 2019-07-06 11:20:32

sum(m) - sum(n-1) can be negative because sum(m) & sum(n-1) are not real answers but instead (real answer)%MOD and there is a possibility that sum(n-1) will be greater than sum(m). So, do ((sum(m)-sum(n-1)%MOD)%MOD which will handle both +ve and -ve numbers. Learnt Matrix Exponentiation because of this !!!

code_breaker11: 2019-06-17 22:29:16

At last...was fed up with rte.

sng_shivang: 2019-06-07 18:59:27

Negative cases are possible so beware of that.

toolatetostart: 2019-05-28 15:14:26

can be done using partial sum
no matrux expo. needed

crackeree: 2019-05-02 11:24:23

This is too much cheap!! :/ "N<=M" has been said in constrain. But further they have set input against the constrain in order to make the problem a bit harder. Negative answers never be possible if N<=M. But using this "cout<<(fibonacci(b+2)-fibonacci(a+1)+mod)%mod<<endl; " instead of "cout<<fibonacci(b+2)-fibonacci(a+1)<<endl; " got AC.

marethyu1: 2018-12-10 20:50:22

I got segmentation fault, please help!


Added by:David Gómez
Date:2010-12-04
Time limit:0.838s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ASM64
Resource:My Own