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Points: 1
Time limit: 1.0s
Memory limit: 256M
Input: stdin
Output: stdout

Author:
Problem type
Allowed languages
C++, Pascal, pypy3, Python

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:

(1,1,1), (1,1,2), (1,2,1), (2,1,1).

The triplets for the second test case 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), (3,1,1).

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