description: 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.
solution: import java.util.*;
  import java.io.*;
  
  public class B_1581 {
  	public static void main(String[] args) throws Exception {
  		Scanner sc = new Scanner(System.in);
  		PrintWriter pw = new PrintWriter(System.out);
  		
  		int t = sc.nextInt();
  		while(t-->0) {
  			int n = sc.nextInt(), m = sc.nextInt(), k = sc.nextInt();
  			long min = n - 1, max = 1l * n * (n - 1) / 2;
  			if(m < min || m > max)
  				pw.println("NO");
  			else {
  				if(n == 1)
  					pw.println(k >= 2 ? "YES" : "NO");
  				else
  					if(m == max)
  						pw.println(k >= 3 ? "YES" : "NO");
  					else
  						pw.println(k >= 4 ? "YES" : "NO");
  			}
  		}
  		
  		pw.flush();
  	}
  
  	public static class Scanner {
  		StringTokenizer st;
  		BufferedReader br;
  
  		public Scanner(InputStream system) {
  			br = new BufferedReader(new InputStreamReader(system));
  		}
  
  		public Scanner(String file) throws Exception {
  			br = new BufferedReader(new FileReader(file));
  		}
  
  		public String next() throws IOException {
  			while (st == null || !st.hasMoreTokens())
  				st = new StringTokenizer(br.readLine());
  			return st.nextToken();
  		}
  
  		public String nextLine() throws IOException {
  			return br.readLine();
  		}
  
  		public int nextInt() throws IOException {
  			return Integer.parseInt(next());
  		}
  
  		public double nextDouble() throws IOException {
  			return Double.parseDouble(next());
  		}
  
  		public char nextChar() throws IOException {
  			return next().charAt(0);
  		}
  
  		public long nextLong() throws IOException {
  			return Long.parseLong(next());
  		}
  
  		public int[] nextIntArray(int n) throws IOException {
  			int[] array = new int[n];
  			for (int i = 0; i < n; i++)
  				array[i] = nextInt();
  			return array;
  		}
  
  		public Integer[] nextIntegerArray(int n) throws IOException {
  			Integer[] array = new Integer[n];
  			for (int i = 0; i < n; i++)
  				array[i] = new Integer(nextInt());
  			return array;
  		}
  
  		public long[] nextLongArray(int n) throws IOException {
  			long[] array = new long[n];
  			for (int i = 0; i < n; i++)
  				array[i] = nextLong();
  			return array;
  		}
  
  		public double[] nextDoubleArray(int n) throws IOException {
  			double[] array = new double[n];
  			for (int i = 0; i < n; i++)
  				array[i] = nextDouble();
  			return array;
  		}
  
  		public static int[] shuffle(int[] a) {
  			int n = a.length;
  			Random rand = new Random();
  			for (int i = 0; i < n; i++) {
  				int tmpIdx = rand.nextInt(n);
  				int tmp = a[i];
  				a[i] = a[tmpIdx];
  				a[tmpIdx] = tmp;
  			}
  			return a;
  		}
  
  		public boolean ready() throws IOException {
  			return br.ready();
  		}
  
  		public void waitForInput() throws InterruptedException {
  			Thread.sleep(3000);
  		}
  	}
  }
  