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.
assistant
#Here is Python code to print T answers — one per test case.

# ------------------- fast io --------------------
import os
import sys
from io import BytesIO, IOBase
 
BUFSIZE = 8192
 
class FastIO(IOBase):
    newlines = 0
    def __init__(self, file):
        self._fd = file.fileno()
        self.buffer = BytesIO()
        self.writable = "x" in file.mode or "r" not in file.mode
        self.write = self.buffer.write if self.writable else None
 
    def read(self):
        while True:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            if not b:
                break
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines = 0
        return self.buffer.read()
 
    def readline(self):
        while self.newlines == 0:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            self.newlines = b.count(b"\n") + (not b)
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines -= 1
        return self.buffer.readline()
 
    def flush(self):
        if self.writable:
            os.write(self._fd, self.buffer.getvalue())
            self.buffer.truncate(0), self.buffer.seek(0)
 
 
class IOWrapper(IOBase):
    def __init__(self, file):
        self.buffer = FastIO(file)
        self.flush = self.buffer.flush
        self.writable = self.buffer.writable
        self.write = lambda s: self.buffer.write(s.encode("ascii"))
        self.read = lambda: self.buffer.read().decode("ascii")
        self.readline = lambda: self.buffer.readline().decode("ascii")
 
 
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")
 
# ------------------- fast io --------------------

import math
testcases=int(input())

for j in range(testcases):
    n,d=list(map(int,input().split()))
    #consider up to sqrt(d)
    found=False
    for s in range(math.ceil(math.sqrt(d))+1):
        if...