Mr. Ant and His Problem

Limits 1s, 512 MB

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 starts with an integer T (1 ≤ T ≤ 1000000), denoting the number of test cases. Each test case contains two integers X and Y (1 ≤ X ≤ Y ≤ 1000000).


For each test case, print the required answer modulo 1000000007.


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This problem was authored for CodeMask Championship 2016 and is being hosted on Toph per organizer’s request.