Competitive Programming #3: [Summed Matrix]

Here is the problem: 
 
A matrix is constructed of size n*n. such that Mi,j= i+j.Count the number of cells having value q. Assume, 1 based indexing.

Input:
The first line contains an integer T , the number of tescases.
Then each test case contains an integer n- size of the matrix , q- whose count you need to tell.

Output:
For every testcase, Output the count of q.

Constraints:
1<=T<=100
1<=n<=1000000000000000(10^16)
2<=q<=2*n

Example:
Input:
2
4 7
5 4
Output:
2
3


Explanation:
1st testcase- Matrix becomes
2 3 4 5
3 4 5 6
4 5 6 7
5 6 7 8
The count of 7 is 2
2nd testcase-Matrix becomes
2 3 4 5 6
3 4 5 6 7
4 5 6 7 8
5 6 7 8 9
6 7 8 9 10
The count of 4 is 3
Solution:
Interesting problem ...It is more math (Math is fun :D)
You can solve this problem with Time Complexity O(1);
Input N is very very very big 10^16 , you should  use unsigned long long int (0 - 18,446,744,073,709,551,615)
So let's see the logic (algorithm)






  Here is a example :