CF1996D Fun

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 $ .

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 $ .

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 $ ).