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.BigDecimal;
  import java.math.*;
  
  public class Main{
  	static int min=Integer.MAX_VALUE;
  	public static void main(String[] args) {
  	    
  	      TaskA solver = new TaskA();
  	      
  	      int t = in.nextInt();
  	      for (int i = 1; i <= t ; i++) {
  	          solver.solve(i, in, out);
  	      }
  	     
  	      
  //	      solver.solve(1, in, out);
  	      
  	      
  	      out.flush();
  	    out.close();
  	  }
  	
  	static Set<Integer>[]graph;
  	 static class TaskA {
  	      public void solve(int testNumber, InputReader in, PrintWriter out) {
  	    		 long n= in.nextInt();
  	    		 long m= in.nextInt();
  	    		 long k =in.nextInt();
  	    		 
  	    		 if(m<n-1||m>(n*(n-1)/2)) {println("NO");return;}
  	    		 
  	    		 if(n==1) {if(k>1) {println("YES");}else{println("NO");}}
  	    		 else if(m<(n*(n-1)/2)) {if(k>3) {println("YES");return;}else{println("NO");return;}
  	    		 }
  	    		 else if(k>2) {println("YES");}
  	    		 else {println("NO");}
  	      }
  	 }
  	static void dfs(int curr,int par) {
  		if(graph[curr].size()==1) {
  			
  		}
  	}
  	 static int[] shift (int[]inp,int i,int j){
  		 int[]arr=new int[j-i+1];
  		 int n=j-i+1;
  		 for(int k=i;k<=j;k++) {
  			 arr[(k-i+1)%n]=inp[k];
  		 }
  		 for(int k=0;k<n;k++ ) {
  			 inp[k+i]=arr[k];
  		 }
  		 return inp;
  	 }
  	 static int sumDigits(long n) {
  		 int total=0;
  		 while(n!=0) {
  			 total+=n%10;
  			 n=n/10;
  		 }
  		 return total;
  	 }
  	 
  	 static long[] fac;
  	    static long mod = (long) 998244353;
  	 
  	    static void initFac(long n) {
  	        fac = new long[(int)n + 1];
  	        fac[0] = 1;
  	        for (int i = 1; i <= n; i++) {
  	            fac[i] = (fac[i - 1]  * i) % mod;
  	        }
  	    }
  	 
  	 
  	 
  	    static long nck(int n, int k) {
  	        if (n < k)
  	            return 0;
  	        long den = inv((int) (fac[k] * fac[n - k] % mod));
  	        return fac[n] * den % mod;
  	    }
  	 
  	    static long pow(long b, long e) {
  	        long ans = 1;
  	        while (e > 0) {
  	            if (e % 2 == 1)
  	                ans = ans * b % mod;
  	            e >>= 1;
  	            b = b * b % mod;
  	        }
  	        return ans;
  	    }
  	 
  	    static long inv(long x) {
  	        return pow(x, mod - 2);
  	    }
  	 
  	 
  	    static void sort(int[] a) {
  	        ArrayList<Integer> q = new ArrayList<>();
  	        for (int i : a) q.add(i);
  	        Collections.sort(q);
  	        for (int i = 0; i < a.length; i++) a[i] = q.get(i);
  	    }
  	 
  	    static void sort(long[] a) {
  	        ArrayList<Long> q = new ArrayList<>();
  	        for (long i : a) q.add(i);
  	        Collections.sort(q);
  	        for (int i = 0; i < a.length; i++) a[i] = q.get(i);
  	    }
  	    
  	 public static int bfsSize(int source,LinkedList<Integer>[]a,boolean[]visited) {
  			Queue<Integer>q=new LinkedList<>();
  			q.add(source);
  			visited[source]=true;
  			int distance=0;
  			while(!q.isEmpty()) {
  				int curr=q.poll();
  				distance++;
  				for(int neighbour:a[curr]) {
  					if(!visited[neighbour]) {
  						visited[neighbour]=true;
  						q.add(neighbour);
  					}
  				}
  			}
  			return distance;
  		}
  	 public static Set<Integer>factors(int n){
  		 Set<Integer>ans=new HashSet<>();
  		 ans.add(1);
  		 for(int i=2;i*i<=n;i++) {
  			 if(n%i==0) {
  				 ans.add(i);
  				 ans.add(n/i);
  			 }
  		 }
  		 return ans;
  	 }
  	public static int bfsSp(int source,int destination,ArrayList<Integer>[]a) {
  		boolean[]visited=new boolean[a.length];
  		int[]parent=new int[a.length];
  		Queue<Integer>q=new LinkedList<>();
  		int distance=0;
  		q.add(source);
  		visited[source]=true;
  		parent[source]=-1;
  		while(!q.isEmpty()) {
  			int curr=q.poll();
  			if(curr==destination) {
  				break;
  			}
  			for(int neighbour:a[curr]) {
  				if(neighbour!=-1&&!visited[neighbour]) {
  					visited[neighbour]=true;
  					q.add(neighbour);
  					parent[neighbour]=curr;
  				}
  			}
  		}
  		int cur=destination;
  		while(parent[cur]!=-1) {
  			distance++;
  			cur=parent[cur];
  		}
  		return distance;
  	}
  	 static int bs(int size,int[]arr) {
  		 int x = -1;
      	 for (int b = size/2; b >= 1; b /= 2) {
          	 while (!ok(arr));
          	 }
      	 int k = x+1;
      	 return k;
  	 }
  	 
  	 static boolean ok(int[]x) {
  		 return false;
  	 }
  	 
  	 public static int solve1(ArrayList<Integer> A) {
  		 long[]arr =new long[A.size()+1];
  		 int n=A.size();
  		 for(int i=1;i<=A.size();i++) {
  			 arr[i]=((i%2)*((n-i+1)%2))%2;
  			 arr[i]%=2;
  		 }
  		 int ans=0;
  		 for(int i=0;i<A.size();i++) {
  			 if(arr[i+1]==1) {
  				 ans^=A.get(i);
  			 }
  		 }
  		 return ans;
  	   }
  	 
  	     public static String printBinary(long a) {
  	    	 String str="";
  	    	 for(int i=31;i>=0;i--) {
  	    		 if((a&(1<<i))!=0) {
  	    			 str+=1;
  	    		 }
  	    		 
  	    		 if((a&(1<<i))==0 && !str.isEmpty()) {
  	    			 str+=0;
  	    		 }
  	    		 
  	    	 }
  	    	 return str;
  	     }
  	     
  		 public static String reverse(long a) {
  		        long rev=0;
  		        String str="";
  		        int x=(int)(Math.log(a)/Math.log(2))+1;
  		        for(int i=0;i<32;i++) {
  		        	rev<<=1;
  		        	if((a&(1<<i))!=0) {
  		        		rev|=1;
  		        		str+=1;
  		        	}
  		        	else {
  		        		str+=0;
  		        	}
  		        }
  		        return str;
  			}
  		
  	 
  	 ////////////////////////////////////////////////////////
  	 static void sortF(Pair arr[])
  	    {
  	        // Comparator to sort the pair according to second element
  	        Arrays.sort(arr, new Comparator<Pair>() {
  	            @Override public int compare(Pair p1, Pair p2)
  	            {	if(p1.first==p2.first) {
  	            	return p1.second-p2.second;
  	            }
  	                return p1.first - p2.first;
  	            }
  	        });
  	    }
  	 static void sortS(Pair arr[])
  	    {
  	        // Comparator to sort the pair according to second element
  	        Arrays.sort(arr, new Comparator<Pair>() {
  	            @Override public int compare(Pair p1, Pair p2)
  	            {
  	                return p1.second - p2.second;
  	            }
  	        });
  	    }
  	 
  	 static class Pair implements Comparable<Pair>
  	 {
  	   int first ;int second  ;
  	  
  	   public  Pair(int x, int y)
  	   {
  	       this.first = x ;this.second = y ;
  	   }
  	   
  	   @Override
  	  public boolean equals(Object obj)
  	  {
  	      if(obj == this)return true  ;
  	      
  	      if(obj == null)return false  ;
  	      
  	      if(this.getClass() != obj.getClass()) return false ;
  	      
  	      Pair other  = (Pair)(obj) ;
  	      
  	      if(this.first != other.first)return false  ;
  	      if(this.second != other.second)return false  ;
  	      
  	      return true  ;
  	      
  	  }
  	     
  	     @Override
  	     
  	     public int hashCode()
  	     {
  	         return this.first^this.second  ;
  	     }
  	       
  	 @Override
  	 	public String toString() {
  	 	
  	 	String ans = "" ;ans  += this.first ;	ans += " ";	ans += this.second ;
  	 	return ans  ;
  	 	}
  
  	
  
  	@Override
  	public int compareTo(Main.Pair o) {
  		{	if(this.first==o.first) {
          	return this.second-o.second;
          }
              return this.first - o.first;
          }
  	}
  	 	
  
  	 }
  	 //////////////////////////////////////////////////////////////////////////
  	
  	    
  	 
  	
  	 static int nD(long num) {
  		 String s=String.valueOf(num);
  		 return s.length();
  	 }
  	 
  	 
  	 static int CommonDigits(int x,int y) {
  		 String s=String.valueOf(x);
  		 String s2=String.valueOf(y);
  		 return 0;
  	 }
  	 
  	 
  	 
  	 static int lcs(String str1, String str2, int m, int n)
  	    {
  	        int L[][] = new int[m + 1][n + 1];
  	        int i, j;
  	 
  	        // Following steps build L[m+1][n+1] in
  	        // bottom up fashion. Note that L[i][j]
  	        // contains length of LCS of str1[0..i-1]
  	        // and str2[0..j-1]
  	        for (i = 0; i <= m; i++) {
  	            for (j = 0; j <= n; j++) {
  	                if (i == 0 || j == 0)
  	                    L[i][j] = 0;
  	 
  	                else if (str1.charAt(i - 1)
  	                         == str2.charAt(j - 1))
  	                    L[i][j] = L[i - 1][j - 1] + 1;
  	 
  	                else
  	                    L[i][j] = Math.max(L[i - 1][j],
  	                                       L[i][j - 1]);
  	            }
  	        }
  	 
  	        // L[m][n] contains length of LCS
  	        // for X[0..n-1] and Y[0..m-1]
  	        return L[m][n];
  	    }
  	 
  	 /////////////////////////////////
  	 boolean IsPowerOfTwo(int x)
  	 {
  	     return (x != 0) && ((x & (x - 1)) == 0);
  	 }
  	 ////////////////////////////////
  	 
  	 static long power(long a,long b,long m ) {
  		 long ans=1;
  		 while(b>0) {
  			 if(b%2==1) {
  				 ans=((ans%m)*(a%m))%m; b--;
  			 }
  			 else {
  				 a=(a*a)%m;b/=2;
  			 }
  			 
  		 }
  		 return ans%m;
  	 }
  	 ///////////////////////////////
  	 public static boolean repeatedSubString(String string) {
  		    return ((string + string).indexOf(string, 1) != string.length());
  		}
  	 static int search(char[]c,int start,int end,char x) {
  		 for(int i=start;i<end;i++) {
  			 if(c[i]==x) {return i;}
  		 }
  		 return -2;
  	 }
  	 ////////////////////////////////
  	 
  	
  	 
  	 static int gcd(int a, int b) {
  	        while (b != 0) {
  	            int t = b;
  	            b = a % b;
  	            a = t;
  	        }
  	        return a;
  	    }
  	
  	 
  	
  	 
  	 static long fac(long a)
  	 {
  	     if(a== 0L || a==1L)return 1L ;
  	     
  	     return a*fac(a-1L) ;
  	 }
  	 
  	 
  	 
  	 static ArrayList al() {
  		 ArrayList<Integer>a =new ArrayList<>();
  			return a;
  		}
  	 
  	static HashSet h() {
  			return new HashSet<Integer>();
  		}
  	static void debug(int[][]a) {
  		int n= a.length;
  		for(int i=1;i<=n;i++) {
  	  		for(int j=1;j<=n;j++) {
  	  			out.print(a[i][j]+" ");
  	  		}
  	  		out.print("\n");
  	  	}
  	}
  	static void debug(int[]a) {
  			out.println(Arrays.toString(a));
  		}
  	
  	static void debug(ArrayList<Integer>a) {
  				out.println(a.toString());
  		}
  	
  	static boolean[]seive(int n){
  		boolean[]b=new boolean[n+1];
  		 for (int i = 2; i <= n; i++)
  	            b[i] = true;
  		 
  		for(int i=2;i*i<=n;i++) {
  			if(b[i]) {
  				for(int j=i*i;j<=n;j+=i) {
  					b[j]=false;
  				}
  			}
  		}
  		return b;
  	}
  	
  	 static int longestIncreasingSubseq(int[]arr) {
  		  int[]sizes=new int[arr.length];
  		  Arrays.fill(sizes, 1);
  		  int max=1;
  		  for(int i=1;i<arr.length;i++) {
  			  for(int j=0;j<i;j++) {
  				  if(arr[j]<arr[i]) {
  					  sizes[i]=Math.max(sizes[i],sizes[j]+1);
  					  max=Math.max(max, sizes[i]);
  				  }
  			  }
  		  }
  		  return max;
  	 }
  	 
  	 public static ArrayList primeFactors(long n)
  	    {
  		    ArrayList<Long>h= new ArrayList<>();
  	        // Print the number of 2s that divide n
  	        if(n%2 ==0) {h.add(2L);}
  	 
  	        // n must be odd at this point.  So we can
  	        // skip one element (Note i = i +2)
  	        for (long i = 3; i <= Math.sqrt(n); i+= 2)
  	        {
  	            if(n%i==0) {h.add(i);}
  	        }
  	        if (n > 2)
  	            h.add(n);
  	        return h;
  	    }
  	 
  	 static boolean Divisors(long n){
  		 if(n%2==1) {
  			 return true;
  		 }
  	     for (long i=2; i<=Math.sqrt(n); i++){
  	            if (n%i==0 && i%2==1){
  	                   return true;
  	            } 
  	        }
  	     return false;
  	    }
  	
  	static InputStream inputStream = System.in;
      static OutputStream outputStream = System.out;
      static InputReader in = new InputReader(inputStream);
      static PrintWriter out = new PrintWriter(outputStream);
      
      public static void superSet(int[]a,ArrayList<String>al,int i,String s) {
      	if(i==a.length) {
      		al.add(s);
      		return;
      	}
      	superSet(a,al,i+1,s);
      	superSet(a,al,i+1,s+a[i]+" ");
      }
      
  	public static long[] makeArr() {
  		long size=in.nextInt();
  		long []arr=new long[(int)size];
  		for(int i=0;i<size;i++) {
  			arr[i]=in.nextInt();
  		}
  		return arr;
  	}
  	
  	public static long[] arr(int n) {
  		long []arr=new long[n+1];
  		for(int i=1;i<n+1;i++) {
  			arr[i]=in.nextLong();
  		}
  		return arr;
  	}
  	
    public static void sort(long arr[], int l, int r)
    {
        if (l < r)
        {
            // Find the middle point
            int m = (l+r)/2;
  
            // Sort first and second halves
            sort(arr, l, m);
            sort(arr , m+1, r);
  
            // Merge the sorted halves
            merge(arr, l, m, r);
        }
    }
  
    static void print(int c) {
  		 out.print(c);
  	 }
  	 static void println(int x) {
  		 out.println(x);
  	 }
  	 static void print(String s) {
  		 out.print(s);
  	 }
  	 static void println(String s) {
  		 out.println(s);
  	 }
  public static void merge(long arr[], int l, int m, int r)
    {
        // Find sizes of two subarrays to be merged
        int n1 = m - l + 1;
        int n2 = r - m;
  
        /* Create temp arrays */
        long L[] = new long[n1];
        long R[] = new long[n2];
  
        //Copy data to temp arrays
        for (int i=0; i<n1; ++i)
            L[i] = arr[l + i];
        for (int j=0; j<n2; ++j)
            R[j] = arr[m + 1+ j];
  
  
        /* Merge the temp arrays */
  
        // Initial indexes of first and second subarrays
        int i = 0, j = 0;
  
        // Initial index of merged subarry array
        int k = l;
        while (i < n1 && j < n2)
        {
            if (L[i] <= R[j])
            {
                arr[k] = L[i];
                i++;
            }
            else
            {
                arr[k] = R[j];
                j++;
            }
            k++;
        }
  
        /* Copy remaining elements of L[] if any */
        while (i < n1)
        {
            arr[k] = L[i];
            i++;
            k++;
        }
  
        /* Copy remaining elements of R[] if any */
        while (j < n2)
        {
            arr[k] = R[j];
            j++;
            k++;
        }
    }
  
  public static void reverse(int[] array)
  {
      int n = array.length;
      for (int i = 0; i < n / 2; i++) {
          int temp = array[i];
          array[i] = array[n - i - 1];
          array[n - i - 1] = temp;
      }
  }
  
    public static long nCr(int n,int k)
    {
        long ans=1L;
        k=k>n-k?n-k:k;
       
        for( int j=1;j<=k;j++,n--)
        {
            if(n%j==0)
            {
                ans*=n/j;
            }else
            if(ans%j==0)
            {
                ans=ans/j*n;
            }else
            {
                ans=(ans*n)/j;
            }
        }
        return ans;
    }
  
    static int searchMax(int index,long[]inp) {
  	  while(index+1<inp.length &&inp[index+1]>inp[index]) {
  		  index+=1;
  	  }
  	  return index;
    }
    static int searchMin(int index,long[]inp) {
  	  while(index+1<inp.length &&inp[index+1]<inp[index]) {
  		  index+=1;
  	  }
  	  return index;
    }
    public class ListNode {
  	       int val;
  	       ListNode next;
  	       ListNode() {}
  	       ListNode(int val) { this.val = val; }
  	       ListNode(int val, ListNode next) { this.val = val; this.next = next; }
  	   }
    static class Pairr implements Comparable<Pairr>{
  		 private int index;
  		 private int cumsum;
  		 private ArrayList<Integer>indices;
  		 public Pairr(int index,int cumsum) {
  			 this.index=index;
  			 this.cumsum=cumsum;
  			 indices=new ArrayList<Integer>();
  		 }
  		 public int compareTo(Pairr other) {
  			 return Integer.compare(cumsum, other.cumsum);
  		 }
  	 }
  	 
    
    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;
  
        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }
  
        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }
  
        public int nextInt() {
            return Integer.parseInt(next());
        }
        public long nextLong() {
      	  return Long.parseLong(next());
        }
    }
  }