ANTP  Mr. Ant & His Problem
Mr. Ant has 3 boxes and the infinite number of marbles. Now he wants to know the number of ways he can put marbles in these three boxes when the following conditions hold.
1) Each box must contain at least 1 marble.
2) The summation of marbles of the 3 boxes must be in between X and Y inclusive.
Now you are given X and Y. You have to find the number of ways Mr. Ant can put marbles in the 3 boxes.
Input
Input starts with an integer T, denoting the number of test cases. Each test case contains two integers X and Y.
Constraints
1<=T<=1000000
1<=X<= Y<=1000000
Output
For each test case, print the required answer modulo 1000000007.
Sample Input 
Sample Output 
1 4 5 
9 
Explanation for the first test case
1  1  2 
Way 01
1  1  3 
Way 02
1  2  1 
Way 03
1  3  1 
Way 04
2  1  1 
Way 05
3  1  1 
Way 06
1  2  2 
Way 07
2  1  2 
Way 08
2  2  1 
Way 09
Note: use faster i/o method.
Problem Setter: Md Abdul Alim, CEO & Founder at CodeMask
hide comments
nimphy:
20180429 04:39:46
I want to know FFT is ok?


Sidharth Sikri:
20160814 15:37:20
can someone tell me, why am i getting a WA for my code  http://ideone.com/4POTiA


nhari:
20160521 18:18:47
5


pankaj joshi:
20160413 18:46:22
Last edit: 20160414 06:36:10 

lalit_nit2:
20160411 00:18:02
intersting but irritating ..(^_^) 

aditya730:
20160404 16:03:31
Last edit: 20160404 16:39:47 

Jitesh:
20160403 16:50:44
@aqua_regia. answer will be 0. 

aqua_regia:
20160403 10:57:58
Are there any special test cases. What if x=1 y=2 ? Is the answer 0 or 1. And provide some additional test cases. 
Added by:  Md Abdul Alim 
Date:  20160401 
Time limit:  1s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ASM64 GOSU JSMONKEY 
Resource:  Own Problem 