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.io.*;
  import java.util.*;
  import java.math.*;
  import java.lang.*;
  
  public class B_Diameter_of_Graph implements Runnable {
      static class InputReader {
          private InputStream stream;
          private byte[] buf = new byte[1024];
          private int curChar;
          private int numChars;
          private SpaceCharFilter filter;
          private BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
  
          public InputReader(InputStream stream) {
              this.stream = stream;
          }
  
          public int read() {
              if (numChars == -1)
                  throw new InputMismatchException();
  
              if (curChar >= numChars) {
                  curChar = 0;
                  try {
                      numChars = stream.read(buf);
                  } catch (IOException e) {
                      throw new InputMismatchException();
                  }
  
                  if (numChars <= 0)
                      return -1;
              }
              return buf[curChar++];
          }
  
          public String nextLine() {
              String str = "";
              try {
                  str = br.readLine();
              } catch (IOException e) {
                  e.printStackTrace();
              }
              return str;
          }
  
          public int nextInt() {
              int c = read();
  
              while (isSpaceChar(c))
                  c = read();
  
              int sgn = 1;
  
              if (c == '-') {
                  sgn = -1;
                  c = read();
              }
  
              int res = 0;
              do {
                  if (c < '0' || c > '9')
                      throw new InputMismatchException();
                  res *= 10;
                  res += c - '0';
                  c = read();
              } while (!isSpaceChar(c));
  
              return res * sgn;
          }
  
          public long nextLong() {
              int c = read();
              while (isSpaceChar(c))
                  c = read();
              int sgn = 1;
              if (c == '-') {
                  sgn = -1;
                  c = read();
              }
              long res = 0;
  
              do {
                  if (c < '0' || c > '9')
                      throw new InputMismatchException();
                  res *= 10;
                  res += c - '0';
                  c = read();
              } while (!isSpaceChar(c));
              return res * sgn;
          }
  
          public double nextDouble() {
              int c = read();
              while (isSpaceChar(c))
                  c = read();
              int sgn = 1;
              if (c == '-') {
                  sgn = -1;
                  c = read();
              }
              double res = 0;
              while (!isSpaceChar(c) && c != '.') {
                  if (c == 'e' || c == 'E')
                      return res * Math.pow(10, nextInt());
                  if (c < '0' || c > '9')
                      throw new InputMismatchException();
                  res *= 10;
                  res += c - '0';
                  c = read();
              }
              if (c == '.') {
                  c = read();
                  double m = 1;
                  while (!isSpaceChar(c)) {
                      if (c == 'e' || c == 'E')
                          return res * Math.pow(10, nextInt());
                      if (c < '0' || c > '9')
                          throw new InputMismatchException();
                      m /= 10;
                      res += (c - '0') * m;
                      c = read();
                  }
              }
              return res * sgn;
          }
  
          public String readString() {
              int c = read();
              while (isSpaceChar(c))
                  c = read();
              StringBuilder res = new StringBuilder();
              do {
                  res.appendCodePoint(c);
                  c = read();
              } while (!isSpaceChar(c));
  
              return res.toString();
          }
  
          public boolean isSpaceChar(int c) {
              if (filter != null)
                  return filter.isSpaceChar(c);
              return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
          }
  
          public String next() {
              return readString();
          }
  
          public interface SpaceCharFilter {
              public boolean isSpaceChar(int ch);
          }
      }
  
      public static void main(String args[]) throws Exception {
          new Thread(null, new B_Diameter_of_Graph(), "Main", 1 << 27).start();
      }
  
      static class Pair {
          int f;
          int s;
          int p;
          PrintWriter w;
  
          // int t;
  
          Pair(int f, int s) {
              // Pair(int f,int s, PrintWriter w){
              this.f = f;
              this.s = s;
              // this.p = p;
              // this.w = w;
              // this.t = t;
  
          }
  
          public static Comparator<Pair> wc = new Comparator<Pair>() {
              public int compare(Pair e1,Pair e2){
  
                  // 1 for swap
                  if(Math.abs(e1.f)-Math.abs(e2.f)!=0){
                      // e1.w.println("**"+e1.f+" "+e2.f);
                      return (Math.abs(e1.f)-Math.abs(e2.f));
                  }
                  else{
                      // e1.w.println("##"+e1.f+" "+e2.f);
                      return (Math.abs(e1.s)-Math.abs(e2.s));
                  }
  
  
              }
          };
      }
  
      public Integer[] sort(Integer[] a) {
          Arrays.sort(a);
          return a;
      }
  
      public Long[] sort(Long[] a) {
          Arrays.sort(a);
          return a;
      }
  
      public static ArrayList<Integer> sieve(int N) {
          int i, j, flag;
  
          ArrayList<Integer> p = new ArrayList<Integer>();
  
          for (i = 1; i < N; i++) {
  
              if (i == 1 || i == 0)
                  continue;
  
              flag = 1;
  
              for (j = 2; j <= i / 2; ++j) {
                  if (i % j == 0) {
                      flag = 0;
                      break;
                  }
              }
              if (flag == 1) {
                  p.add(i);
              }
          }
          return p;
      }
  
      public static long gcd(long a, long b) {
          if (b == 0)
              return a;
          else
              return gcd(b, a % b);
      }
  
      public static int gcd(int a, int b) {
          if (b == 0)
              return a;
          else
              return gcd(b, a % b);
      }
  
      //// recursive dfs
      public static int dfs(int s, ArrayList<Integer>[] g, long[] dist, boolean[] v, PrintWriter w, int p) {
          v[s] = true;
          int ans = 1;
          // int n = dist.length - 1;
          int t = g[s].size();
          // int max = 1;
          for (int i = 0; i < t; i++) {
              int x = g[s].get(i);
              if (!v[x]) {
                  // dist[x] = dist[s] + 1;
                  ans = Math.min(ans, dfs(x, g, dist, v, w, s));
              } else if (x != p) {
                  // w.println("* " + s + " " + x + " " + p);
                  ans = 0;
              }
          }
          // max = Math.max(max,(n-p));
          return ans;
      }
  
      //// iterative BFS
      public static int bfs(int s, ArrayList<Integer>[] g, long[] dist, boolean[] b, PrintWriter w, int p) {
          b[s] = true;
          int siz = 1;
          // dist--;
          Queue<Integer> q = new LinkedList<>();
          q.add(s);
          while (q.size() != 0) {
              int i = q.poll();
              Iterator<Integer> it = g[i].listIterator();
              int z = 0;
              while (it.hasNext()) {
                  z = it.next();
                  if (!b[z]) {
                      b[z] = true;
                      // dist--;
                      dist[z] = dist[i] + 1;
                      // siz++;
                      q.add(z);
                  } else if (z != p) {
                      siz = 0;
                  }
              }
  
          }
          return siz;
      }
  
      public static int lower(int a[], int x) { // x is the target value or key
          int l = -1, r = a.length;
          while (l + 1 < r) {
              int m = (l + r) >>> 1;
              if (a[m] >= x)
                  r = m;
              else
                  l = m;
          }
          return r;
      }
  
      public static int upper(int a[], int x) {// x is the key or target value
          int l = -1, r = a.length;
          while (l + 1 < r) {
              int m = (l + r) >>> 1;
              if (a[m] <= x)
                  l = m;
              else
                  r = m;
          }
          return l + 1;
      }
  
      public static int lower(ArrayList<Integer> a, int x) { // x is the target value or key
          int l = -1, r = a.size();
          while (l + 1 < r) {
              int m = (l + r) >>> 1;
              if (a.get(m) >= x)
                  r = m;
              else
                  l = m;
          }
          return r;
      }
  
      public static int upper(ArrayList<Integer> a, int x) {// x is the key or target value
          int l = -1, r = a.size();
          while (l + 1 < r) {
              int m = (l + r) >>> 1;
              if (a.get(m) <= x)
                  l = m;
              else
                  r = m;
          }
          return l + 1;
      }
  
      public static long power(long x, long y, long m) {
          if (y == 0)
              return 1;
  
          long p = power(x, y / 2, m) % m;
          p = (p * p) % m;
  
          if (y % 2 == 0)
              return p;
          else
              return (x * p) % m;
      }
  
      public void yesOrNo(boolean f) {
          if (f) {
              w.println("YES");
          } else {
              w.println("NO");
          }
      }
  
      // Arrays.sort(rooms, (room1, room2) -> room1[1] == room2[1] ? room1[0]-room2[0]
      // : room2[1]-room1[1]);
      // Arrays.sort(A, (a, b) -> Integer.compare(a[0] , b[0]));
      //////////////////////////////////////////////////////////////////////////////////////////////////////
      //////////////////////////////////////////////////////////////////////////////////////////////////////
      // code here
      int oo = (int) 1e9;
      int[] parent;
      int[] dist;
      int[][] val;
      boolean[][] vis;
      ArrayList<Integer>[] g;
      // int[] col;
      // HashMap<Long, Boolean>[] dp;
      //char[][] g;
      // boolean[][] v;
      Long[] a;
      // ArrayList<Integer[]> a;
      // int[][] ans;
      long[][] dp;
      long mod;
      int n;
      int m;
      int k;
      long[][] pre;
      // StringBuilder[] a;
      // StringBuilder[] b;
      // StringBuilder ans;
      int[][] col;
      int[][] row;
      PrintWriter w = new PrintWriter(System.out);
  
      public void run() {
  
          InputReader sc = new InputReader(System.in);
  
          int defaultValue = 0;
          mod =  1000000007;
  
          int test = 1;
          test = sc.nextInt();
          while (test-- > 0) {
              long n = sc.nextLong();
  			long m = sc.nextLong();
  			long k = sc.nextLong();
  			long max = n*(n-1)/2;
  			if(max<m||n-1>m)
  			    w.println("NO");
  			else if((k<=1 && n==1))
  			      w.println("NO");
  			      else if((k<=2 && n==2))
  			      w.println("NO");
  			      else if(n>=3&&(m<max &&k<=3||n-1>m||m>=max&&k<=2))
  			      w.println("NO");
  			      else
  			      w.println("YES");
  			
          }
  
          w.flush();
          w.close();
  
      }
  }
  
  