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A. Deadline

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputAdilbek 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?

Input

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.

Output

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.

Example

Input

3 1 1 4 5 5 11

Output

YES YES NO

Note

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.

Codeforces (c) Copyright 2010-2023 Mike Mirzayanov

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