CQXYM wants to create a connected undirected graph with n nodes and m edges, and the diameter of the graph must be strictly less than k-1. Also, CQXYM doesn't want a graph that contains self-loops or multiple edges (i.e. each edge connects two different vertices and between each pair of vertices there is at most one edge).

The diameter of a graph is the maximum distance between any two nodes.

The distance between two nodes is the minimum number of the edges on the path which endpoints are the two nodes.

CQXYM wonders whether it is possible to create such a graph.

Input

The input consists of multiple test cases. 

The first line contains an integer t (1 ≤ t ≤ 10^5) — the number of test cases. The description of the test cases follows.

Only one line of each test case contains three integers n(1 ≤ n ≤ 10^9), m, k (0 ≤ m,k ≤ 10^9).

Output

For each test case, print YES if it is possible to create the graph, or print NO if it is impossible. You can print each letter in any case (upper or lower).

Example

Input


5
1 0 3
4 5 3
4 6 3
5 4 1
2 1 1


Output


YES
NO
YES
NO
NO

Note

In the first test case, the graph's diameter equal to 0.

In the second test case, the graph's diameter can only be 2.

In the third test case, the graph's diameter can only be 1.
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import os
import sys
from io import BytesIO, IOBase
#-----------------------IMPORTANT  FUNCTIONS ---------------------------------#
from math import cos, pi, ceil, pi, tan, floor, gcd, sqrt, log2, factorial, log10
from collections import Counter
from copy import deepcopy
from string import ascii_lowercase, ascii_uppercase
from statistics import mean, median, mode
from bisect import *

alpha = ascii_lowercase
beta = ascii_uppercase


#-----------------------NEXT POWER OF 2---------------------------------------#
def nextPowerOf2(n):
    p = 1
    if (n and not (n & (n - 1))):
        return n
    while (p < n):
        p <<= 1
    return p
#-----------------------COMPOSITE  CHECK---------------------------------------#
def isComposite(n):
    if (n <= 1):
        return False
    if (n <= 3):
        return False
    if (n % 2 == 0 or n % 3 == 0):
        return True
    i = 5
    while(i * i <= n):
        if (n % i == 0 or n % (i + 2) == 0):
            return True
        i = i + 6
    return False


#-----------------------GET DIVISORS 1 TO <=N   ------------------------------#
def get_Divisors(n):
    arr = []
    i = 1
    while i <= sqrt(n):
        if (n % i == 0):
            if (n / i == i):
                arr.append(i)
            else:
                arr.append(i)
                arr.append(n // i)
        i = i + 1

    return arr


#----------------------CHECK    PRIMES-----------------------------------#
def isprime(n):
    if n == 1:
        return 0
    i = 2
    while (i * i <= n):
        if (n % i == 0):
            return 0
        i += 1
    return 1


#-----------------------PRE COMPUTED  PRIMES-----------------------------------#
def Sieve(n):
    prime = [True for i in range(n + 1)]
    prime[0] = False
    prime[1] = False
    p = 2
    while (p * p <= n):
        if (prime[p] == True):
            for i in range(p * p, n + 1, p):
                prime[i] = False
        p += 1
    return prime


#-----------------------LARGER VALUE OF  X,Y,10**9+7 --------------------------#
def power(x, y, p):
    res = 1
    x = x % p
    if (x == 0):
        return 0
    while (y > 0):
        if ((y & 1) == 1):
            res = (res * x) % p
        y = y >> 1
        x = (x * x) % p
    return res


#-----------------------       CREATE MATRIX         --------------------------#
def create_matrix(n, m):
    mat = [[] for i in range(n)]
    for i in range(n):
        for j in range(m):
            mat[i].append(0)
    return mat


#By Default Counter stores the value in decending orderCounter({4: 2, 8: 2, 2: 1, 9: 1}
#s=sorted(s.items(),key=lambda k:(k[0],k[1])) ---> [(2, 1), (4, 2), (8, 2), (9, 1)]
#sort 2nd value  from bada se chhota  then(4,2)(8,2)->>(8,2)(4,2) s=sorted(s.items(),key=lambda k:(-k[1],-k[0]))  [(8, 2), (4, 2), (9, 1), (2, 1)]
#for list pair in a list    s.sort(key=lambda k:(-k[1],-k[0])) [[3, 4], [8, 2], [4, 2]]
# from functools import cmp_to_key
#how to use compare ----ss = sorted(s, key=cmp_to_key(compare))
# #-----------------------*****CODE STARTS  HERE*****--------------------------#
# sys.stdout = open('ot.txt', 'w')
# sys.stdin = open('in.txt', 'r')
# from queue import Queue
# from random import *
def main():
    for ttt in range(int(input())):
        n,m,k=map(int,input().split())
        if m<n-1  or m>n*(n-1)//2:
            print("NO")
        elif m==n*(n-1)//2:
            if k>2:
                print("YES")
            else:
                print("NO")
        elif n==1:
            if k>1:
                print("YES")
            else:
                print("NO")
        elif m==n-1:
            if k>4:
                print("YES")
            else:
                print("NO")
        elif n-1<m<n*(n-1)//2:
            if k>3:
                print("YES")
            else:
                print("NO")

# Region Fast_______io
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")
if __name__ == "__main__":
    main()