human
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⌈ (d)/(x + 1) \right⌉ days (\left⌈ a \right⌉ is the ceiling function: \left⌈ 2.4 \right⌉ = 3, \left⌈ 2 \right⌉ = 2). The program cannot be run and optimized simultaneously, so the total number of days he will spend is equal to x + \left⌈ (d)/(x + 1) \right⌉.

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 ≤ T ≤ 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 ≤ n ≤ 10^9, 1 ≤ d ≤ 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 ≤ n.

In the second test case, Adilbek can spend 1 day optimizing the program and it will run \left⌈ 5/2 \right⌉ = 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⌈ (11)/(2+1) \right⌉ = 4 days.
The above is tricky. Write me a correct solution in PYTHON3.
assistant
#Here is Python code to print T answers — one per test case.

# import atexit
# import io
# import sys
#
# _INPUT_LINES = sys.stdin.read().splitlines()
# input = iter(_INPUT_LINES).__next__
# _OUTPUT_BUFFER = io.StringIO()
# sys.stdout = _OUTPUT_BUFFER
#
#
# @atexit.register
# def write():
#     sys.__stdout__.write(_OUTPUT_BUFFER.getvalue())
#####################################################

def num():
    return int(input())
def line():
    return map(int, input().split())

from itertools import repeat

T = num()
for _ in repeat(None, T):
    n,d = line()
    print('YES' if n**2+2*n-4*d+1>=0 else 'NO')