D. Fun
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output
Counting is Fun!
— satyam343

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 $$$0$$$.

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 $$$a + b + c \le x$$$.

Example
Input
4
7 4
10 5
7 1000
900000 400000
Output
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 ($$$3, 1, 1$$$).