human
Can you solve the below in PYTHON3?
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.
 Write me a Python program to print YES if it is possible to create the graph, or print NO if it is impossible?
assistant
#Here is Python program to print YES if it is possible to create the graph, or print NO if it is impossible.

import math
import sys
import operator as op
from functools import reduce
from collections import OrderedDict

class Input:
    @staticmethod
    def string():
        return str(input())

    @staticmethod
    def int():
        return int(input())

    @staticmethod
    def list(sep=' '):
        return input().split(sep)

    @staticmethod
    def list_int(sep=' '):
        return list(map(int, input().split(sep)))

class Output:
    @staticmethod
    def print(res):
        print(res)

    @staticmethod
    def string(res):
        print(str(res))

    @staticmethod
    def list(res):
        print(' '.join(str(x) for x in res))

class Algorithms:
    @staticmethod
    def isPrime(n):
        return all(n % i != 0 for i in range(2, int(math.sqrt(n) + 1)))

    @staticmethod
    def getPrimeNumbers(n):
        a = [1]
        for num in range(2, n):
            if all(num % i != 0 for i in range(2, int(math.sqrt(num) + 1))):
                a.append(num)
        return a

    # Факторизация - Разложение числа на простые множители
    @staticmethod
    def factorization(n):
        res = {}
        for i in range(2, n * n):
            cnt = 0
            while n % i == 0:
                cnt += 1
                n = n / i
            if cnt > 0:
                res[i] = cnt
        if n > 1:
            res[n] = 1
        return res

    # Наибольший общий делитель (НОД)
    @staticmethod
    def gcd(a, b):
        if b == 0:
            return a
        else:
            a = a % b
            return Algorithms.gcd(b, a)

    # Наименьшее общее кратное (НОК)
    @staticmethod
    def lcm(a, b):
        return abs(a * b) // Algorithms.gcd(a, b)

    # Последовательность Фибоначчи =  0, 1, 1, 2, 3, 5, 8, 13, 21, 34
    @staticmethod
    def fibonacci(n):
        a = [0, 1]
        for i in range(2, n + 1):
            a.append(a[i - 1] - a[i - 2])
        return a[n]

    @staticmethod
    def z_func(s):
        n = len(s)
        z = [0] * n
        l = r = 0
        for i in range(1, n):
            if...