Fun
Description
Given two integers $n$ and $x$, find the number of triplets ($a,b,c$) of positive integers such that $ab + ac + bc \le n$ and $a + b + c \le x$.
Note that order matters (e.g. ($1, 1, 2$) and ($1, 2, 1$) are treated as different) and $a$, $b$, $c$ must be strictly greater than $0$.
The first line contains a single integer $t$ ($1 \leq t \leq 10^4$) — the number of test cases.
Each test case contains two integers $n$ and $x$ ($1 \leq n,x \leq 10^6$).
It is guaranteed that the sum of $n$ over all test cases does not exceed $10^6$ and that the sum of $x$ over all test cases does not exceed $10^6$.
Output a single integer — the number of triplets ($a,b,c$) of positive integers such that $ab + ac + bc \le n$ and $a + b + c \le x$.
Input
The first line contains a single integer $t$ ($1 \leq t \leq 10^4$) — the number of test cases.
Each test case contains two integers $n$ and $x$ ($1 \leq n,x \leq 10^6$).
It is guaranteed that the sum of $n$ over all test cases does not exceed $10^6$ and that the sum of $x$ over all test cases does not exceed $10^6$.
Output
Output a single integer — the number of triplets ($a,b,c$) of positive integers such that $ab + ac + bc \le n$ and $a + b + c \le x$.
4
7 4
10 5
7 1000
900000 400000
4
10
7
1768016938
Note
In the first test case, the triplets are ($1, 1, 1$), ($1, 1, 2$), ($1, 2, 1$), and ($2, 1, 1$).
In the second test case, the triplets are ($1, 1, 1$), ($1, 1, 2$), ($1, 1, 3$), ($1, 2, 1$), ($1, 2, 2$), ($1, 3, 1$), ($2, 1, 1$), ($2, 1, 2$), ($2, 2, 1$), and ($3, 1, 1$).