Given two integers $n$ and $x$, your task is to count the number of ordered triplets $(a, b, c)$ of positive integers such that the following conditions are satisfied:

1. $ab + ac + bc \leq n$
2. $a + b + c \leq x$

Notes: $(a, b, c)$ is an triplet, meaning $(1,1,2)$ and $(1,2,1)$ are considered different. $a, b, c > 0$ (each element of the triplet must be strictly greater than zero).

Input:

• The first line contains an integer $t$ ($1 \leq t \leq 10^4$) --- the number of test cases.
• Each test case consists of two integers $n$ and $x$ ($1 \leq n, x \leq 10^6$).
• The sum of all $n$ values across test cases does not exceed $10^6$, and the sum of all $x$ values across test cases does not exceed $10^6$

Output:

• For each test case, print a single integer --- the number of valid triplets $(a, b, c)$.

Example:
Sample Input 1:

 4
 7 4
 10 5
 7 1000
 900000 400000

Sample Output 1:

 4
 10
 7
 1768016938

Notes:
The triplets for the first test case are:

The triplets for the second test case are: