CF1288A Deadline

Adilbek was assigned to a special project. For Adilbek it means that he has $ n $ days to run a special program and provide its results. But there is a problem: the program needs to run for $ d $ days to calculate the results. Fortunately, Adilbek can optimize the program. If he spends $ x $ ( $ x $ is a non-negative integer) days optimizing the program, he will make the program run in $ \left\lceil \frac{d}{x + 1} \right\rceil $ days ( $ \left\lceil a \right\rceil $ is the ceiling function: $ \left\lceil 2.4 \right\rceil = 3 $ , $ \left\lceil 2 \right\rceil = 2 $ ). The program cannot be run and optimized simultaneously, so the total number of days he will spend is equal to $ x + \left\lceil \frac{d}{x + 1} \right\rceil $ . Will Adilbek be able to provide the generated results in no more than $ n $ days?

The first line contains a single integer $ T $ ( $ 1 \le T \le 50 $ ) — the number of test cases. The next $ T $ lines contain test cases – one per line. Each line contains two integers $ n $ and $ d $ ( $ 1 \le n \le 10^9 $ , $ 1 \le d \le 10^9 $ ) — the number of days before the deadline and the number of days the program runs.

Print $ T $ answers — one per test case. For each test case print YES (case insensitive) if Adilbek can fit in $ n $ days or NO (case insensitive) otherwise.

In the first test case, Adilbek decides not to optimize the program at all, since $ d \le n $ . In the second test case, Adilbek can spend $ 1 $ day optimizing the program and it will run $ \left\lceil \frac{5}{2} \right\rceil = 3 $ days. In total, he will spend $ 4 $ days and will fit in the limit. In the third test case, it's impossible to fit in the limit. For example, if Adilbek will optimize the program $ 2 $ days, it'll still work $ \left\lceil \frac{11}{2+1} \right\rceil = 4 $ days.