Given two integers $n$ and $x$, find the number of triplets ($a,b,c$) of positive integers such that $+ ac + bc \le n$ 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 $0$.

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 $+ ac + bc \le n$ and $a + b + c \le x$.

见题面 Input 部分

见题面 Output 部分

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 ($3, 1, 1$).