write a go solution for Description:
This version of the problem differs from the previous one only in the constraint on t. You can make hacks only if both versions of the problem are solved.

You are given two positive integers l and r.

Count the number of distinct triplets of integers (i,j,k) such that l<=i<j<k<=r and operatornamelcm(i,j,k)>=i+j+k.

Here operatornamelcm(i,j,k) denotes the least common multiple (LCM) of integers i, j, and k.

Input Format:
Each test contains multiple test cases. The first line contains the number of test cases t (bf1<=t<=10^5). Description of the test cases follows.

The only line for each test case contains two integers l and r (1<=l<=r<=2*10^5, l+2<=r).

Output Format:
For each test case print one integer — the number of suitable triplets.

Note:
In the first test case, there are 3 suitable triplets:

- (1,2,3),
- (1,3,4),
- (2,3,4).

In the second test case, there is 1 suitable triplet:

- (3,4,5).. Output only the code with no comments, explanation, or additional text.