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.lang.reflect.Array;
  import java.text.DecimalFormat;
  import java.util.*;
  import java.lang.*;
  import java.io.*;
  
  
  public class cf2 {
      static PrintWriter out;
      static int MOD = 1000000007;
      static FastReader scan;
  
      /*-------- I/O using short named function ---------*/
      public static String ns() {
          return scan.next();
      }
  
      public static int ni() {
          return scan.nextInt();
      }
  
      public static long nl() {
          return scan.nextLong();
      }
  
      public static double nd() {
          return scan.nextDouble();
      }
  
      public static String nln() {
          return scan.nextLine();
      }
  
      public static void p(Object o) {
          out.print(o);
      }
  
      public static void ps(Object o) {
          out.print(o + " ");
      }
  
      public static void pn(Object o) {
          out.println(o);
      }
  
      /*-------- for output of an array ---------------------*/
      static void iPA(int arr[]) {
          StringBuilder output = new StringBuilder();
          for (int i = 0; i < arr.length; i++) output.append(arr[i] + " ");
          out.println(output);
      }
  
      static void lPA(long arr[]) {
          StringBuilder output = new StringBuilder();
          for (int i = 0; i < arr.length; i++) output.append(arr[i] + " ");
          out.println(output);
      }
  
      static void sPA(String arr[]) {
          StringBuilder output = new StringBuilder();
          for (int i = 0; i < arr.length; i++) output.append(arr[i] + " ");
          out.println(output);
      }
  
      static void dPA(double arr[]) {
          StringBuilder output = new StringBuilder();
          for (int i = 0; i < arr.length; i++) output.append(arr[i] + " ");
          out.println(output);
      }
  
      /*-------------- for input in an array ---------------------*/
      static void iIA(int arr[]) {
          for (int i = 0; i < arr.length; i++) arr[i] = ni();
      }
  
      static void lIA(long arr[]) {
          for (int i = 0; i < arr.length; i++) arr[i] = nl();
      }
  
      static void sIA(String arr[]) {
          for (int i = 0; i < arr.length; i++) arr[i] = ns();
      }
  
      static void dIA(double arr[]) {
          for (int i = 0; i < arr.length; i++) arr[i] = nd();
      }
  
      /*------------ for taking input faster ----------------*/
      static class FastReader {
          BufferedReader br;
          StringTokenizer st;
  
          public FastReader() {
              br = new BufferedReader(new InputStreamReader(System.in));
          }
  
          String next() {
              while (st == null || !st.hasMoreElements()) {
                  try {
                      st = new StringTokenizer(br.readLine());
                  } catch (IOException e) {
                      e.printStackTrace();
                  }
              }
              return st.nextToken();
          }
  
          int nextInt() {
              return Integer.parseInt(next());
          }
  
          long nextLong() {
              return Long.parseLong(next());
          }
  
          double nextDouble() {
              return Double.parseDouble(next());
          }
  
          String nextLine() {
              String str = "";
              try {
                  str = br.readLine();
              } catch (IOException e) {
                  e.printStackTrace();
              }
              return str;
          }
      }
  
      public static ArrayList<Integer> sieveOfEratosthenes(int n) {
          // Create a boolean array
          // "prime[0..n]" and
          // initialize all entries
          // it as true. A value in
          // prime[i] will finally be
          // false if i is Not a
          // prime, else true.
          boolean prime[] = new boolean[n + 1];
          for (int i = 0; i <= n; i++)
              prime[i] = true;
  
          for (int p = 2; p * p <= n; p++) {
              // If prime[p] is not changed, then it is a
              // prime
              if (prime[p] == true) {
                  // Update all multiples of p
                  for (int i = p * p; i <= n; i += p)
                      prime[i] = false;
              }
          }
          ArrayList<Integer> arr = new ArrayList<>();
          // store all prime numbers
          for (int i = 2; i <= n; i++) {
              if (prime[i] == true)
                  arr.add(i);
          }
          return arr;
      }
  
      // Method to check if x is power of 2
      static boolean isPowerOfTwo(int x) {
          return x != 0 && ((x & (x - 1)) == 0);
      }
  
      //Method to return lcm of two numbers
      static int gcd(int a, int b) {
          return a == 0 ? b : gcd(b % a, a);
      }
  
      //Method to count digit of a number
      static int countDigit(long n) {
          String sex = Long.toString(n);
          return sex.length();
      }
  
      static void reverse(int a[]) {
          int i, k, t;
          int n = a.length;
          for (i = 0; i < n / 2; i++) {
              t = a[i];
              a[i] = a[n - i - 1];
              a[n - i - 1] = t;
          }
      }
      static long nCr(long n, long r)
      {
          long p = 1, k = 1;
  
          // C(n, r) == C(n, n-r),
          // choosing the smaller value
          if (n - r < r) {
              r = n - r;
          }
  
          if (r != 0) {
              while (r > 0) {
                  p *= n;
                  k *= r;
  
                  // gcd of p, k
                  long m = __gcd(p, k);
  
                  // dividing by gcd, to simplify
                  // product division by their gcd
                  // saves from the overflow
                  p /= m;
                  k /= m;
  
                  n--;
                  r--;
              }
  
              // k should be simplified to 1
              // as C(n, r) is a natural number
              // (denominator should be 1 ) .
          }
          else {
              p = 1;
          }
  
          // if our approach is correct p = ans and k =1
          return p;
      }
      static long __gcd(long n1, long n2)
      {
          long gcd = 1;
  
          for (int i = 1; i <= n1 && i <= n2; ++i) {
              // Checks if i is factor of both integers
              if (n1 % i == 0 && n2 % i == 0) {
                  gcd = i;
              }
          }
          return gcd;
      }
  
      // Returns factorial of n
      static long fact(long n)
      {
          long res = 1;
          for (long i = 2; i <= n; i++)
              res = res * i;
          return res;
      }
      // Get all prime numbers till N using seive of Eratosthenes
      public static List<Integer> getPrimesTill(int n){
          boolean[] arr = new boolean[n+1];
          List<Integer> primes = new LinkedList<>();
          for(int i=2; i<=n; i++){
              if(!arr[i]){
                  primes.add(i);
                  for(long j=(i*i); j<=n; j+=i){
                      arr[(int)j] = true;
                  }
              }
          }
          return primes;
      }
  
      static final Random random = new Random();
  
      //Method for sorting
      static void ruffleSort(int[] arr) {
          int n = arr.length;
          for (int i = 0; i < n; i++) {
              int j = random.nextInt(n);
              int temp = arr[j];
              arr[j] = arr[i];
              arr[i] = temp;
          }
          Arrays.sort(arr);
      }
  
      static void sortadv(long[] a) {
          ArrayList<Long> l = new ArrayList<>();
          for (long value : a) {
              l.add(value);
          }
          Collections.sort(l);
          for (int i = 0; i < l.size(); i++)
              a[i] = l.get(i);
      }
  
      //Method for checking if a number is prime or not
      static boolean isPrime(int n) {
          if (n <= 1) return false;
          if (n <= 3) return true;
          if (n % 2 == 0 || n % 3 == 0) return false;
          for (int i = 5; i * i <= n; i = i + 6)
              if (n % i == 0 || n % (i + 2) == 0)
                  return false;
          return true;
      }
  
      public static void main(String[] args) throws java.lang.Exception {
          OutputStream outputStream = System.out;
          out = new PrintWriter(outputStream);
          scan = new FastReader();
          //for fast output sometimes
          StringBuilder sb1 = new StringBuilder();
  
          // prefix sum, *dp , odd-even segregate , *brute force(n=100)(jo bola wo kar) , 2 pointer , pattern , see contraints
          // but first observe!   maybe just watch i-o like ans-x-1,y for input x,y;
          // divide wale ques me always check whether divisor 1?  || probability mei mostly (1-p)...
          // Deque<String> deque = new LinkedList<String>();
          int t = ni();
  
          while (t-- != 0) {
              int n=ni();
              int m=ni();
              int k=ni();
              if(m>=n-1&&m<=((long)(n)*(n-1))/2){
                  int d=0;
                  if(n==1)
                      d=0;
                  else if(m==((long)(n)*(n-1))/2)
                      d=1;
                  else
                      d=2;
                  if(d<k-1)
                      pn("YES");
                  else
                      pn("NO");
              }
              else{
                  pn("NO");
              }
          }
          out.flush();
          out.close();
      }
      public static int modInverse(int a, int m)
      {
          int m0 = m;
          int y = 0, x = 1;
  
          if (m == 1)
              return 0;
  
          while (a > 1) {
              // q is quotient
              int q = a / m;
  
              int t = m;
  
              // m is remainder now, process
              // same as Euclid's algo
              m = a % m;
              a = t;
              t = y;
  
              // Update x and y
              y = x - q * y;
              x = t;
          }
  
          // Make x positive
          if (x < 0)
              x += m0;
  
          return x;
      }
      public static int countodd(int[] a){
          int count=0;
          for(int i:a){
              if(i%2==1)
                  count++;
          }
          return count;
      }
      static int minOps(String s, int si, int ei, char ch) {
  
          if (si == ei) {
              return ch == s.charAt(si) ? 0 : 1;
          }
  
          int mid =( si+ei) >>1;
  
          int leftC = minOps(s, si, mid, (char) (ch + 1));
          int rightC = minOps(s, mid + 1, ei, (char) (ch + 1));
  
          for (int i = si; i <= mid; i++) {
              if (s.charAt(i) != ch)
                  rightC++;
          }
  
          for (int i = mid + 1; i <= ei; i++) {
              if (s.charAt(i) != ch)
                  leftC++;
          }
  
          return Math.min(leftC, rightC);
  
      }
      public static int sumofdigit(long n){
          int sum=0;
          while(n!=0){
              sum+=n%10;
              n/=10;
          }
          return sum;
      }
      public static int computeXOR(int n)
      {
          // If n is a multiple of 4
          if (n % 4 == 0)
              return n;
  
          // If n%4 gives remainder 1
          if (n % 4 == 1)
              return 1;
  
          // If n%4 gives remainder 2
          if (n % 4 == 2)
              return n + 1;
  
          // If n%4 gives remainder 3
          return 0;
      }
      public static class Pair implements Comparable<Pair>{
          int a, b;
          public Pair(int x,int y){
              a=x;b=y;
          }
          @Override
          public int compareTo(Pair o) {
              if(this.a!=o.a)
                  return this.a-o.a;
              else
                  return o.b-this.b;
          }
      }
      private static boolean checkCycle(int node,  ArrayList<ArrayList<Integer>> adj, int vis[], int dfsVis[]) {
          vis[node] = 1;
          dfsVis[node] = 1;
  
          for(Integer it: adj.get(node)) {
              if(vis[it] == 0) {
                  if(checkCycle(it, adj, vis, dfsVis) == true) {
                      return true;
                  }
              } else if(dfsVis[it] == 1) {
                  return true;
              }
          }
          dfsVis[node] = 0;
          return false;
      }
      public static boolean isCyclic(int N, ArrayList<ArrayList<Integer>> adj) {
          int vis[] = new int[N];
          int dfsVis[] = new int[N];
  
          for(int i = 0;i<N;i++) {
              if(vis[i] == 0) {
                  if(checkCycle(i, adj, vis, dfsVis) == true) return true;
              }
          }
          return false;
      }
  }
  
  
  
  