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.

import java.util.*;
import java.util.concurrent.CompletableFuture;

import javax.swing.text.Segment;


import java.io.*;
import java.math.*;
import java.sql.Array;



public class Main {
	  static class Reader{
		  
			BufferedReader br;
			StringTokenizer st;
			public Reader() {
				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; 
		    } 
		}
	 
	  static long mod = (long)(1e9 + 7);
	 
	static void sort(long[] arr ) {
		 ArrayList<Long> al = new ArrayList<>();
		 for(long e:arr) al.add(e);
		 Collections.sort(al);
		 for(int i = 0 ; i<al.size(); i++) arr[i] = al.get(i);
	 }
	static void sort(int[] arr ) {
		 ArrayList<Integer> al = new ArrayList<>();
		 for(int e:arr) al.add(e);
		 Collections.sort(al);
		 for(int i = 0 ; i<al.size(); i++) arr[i] = al.get(i);
	 }
	static void sort(char[] arr) {
		ArrayList<Character> al = new ArrayList<Character>();
		for(char cc:arr) al.add(cc);
		Collections.sort(al);
		for(int i = 0 ;i<arr.length ;i++) arr[i] = al.get(i);
	}
	static void rvrs(int[] arr) {
		int i =0 , j = arr.length-1;
		while(i>=j) {
			int temp = arr[i];
			arr[i] = arr[j];
			arr[j] = temp;
			i++;
			j--;
		}
	}
	static void rvrs(long[] arr) {
		int i =0 , j = arr.length-1;
		while(i>=j) {
			long temp = arr[i];
			arr[i] = arr[j];
			arr[j] = temp;
			i++;
			j--;
		}
	}

	static long mod_mul(long a , long b ,long mod) {
		return ((a%mod)*(b%mod))%mod;
	}
	 static long gcd(long a, long b)
	  {      
	     if (b == 0)
	        return a;
	     return gcd(b, a % b); 
	  }
	 static boolean[] prime(int num) {
			boolean[] bool = new boolean[num];
		     
		      for (int i = 0; i< bool.length; i++) {
		         bool[i] = true;
		      }
		      for (int i = 2; i< Math.sqrt(num); i++) {
		         if(bool[i] == true) {
		            for(int j = (i*i); j<num; j = j+i) {
		               bool[j] = false;
		            }
		         }
		      }
		      if(num >= 0) {
		    	  bool[0] = false;
		    	  bool[1] = false;
		      }
		      
		      return bool;
		}

	 static long modInverse(long a, long m)
	    {
	        long g = gcd(a, m);
	       
	          return   power(a, m - 2, m);
	        
	    }
	   
	 static long power(long x, long y, long m){
	        if (y == 0) return 1; long p = power(x, y / 2, m) % m; p = (int)((p * (long)p) % m);
	        if (y % 2 == 0) return p; else return (int)((x * (long)p) % m); }
	   
     static class Combinations{
	    	 private long[] z;
	    	 private long[] z1;
	    	 private long[] z2;
	    	  public Combinations(long N , long mod) {
				z = new long[(int)N+1];
				z1 = new long[(int)N+1];
				z[0] = 1;
				for(int i =1 ; i<=N ; i++) z[i] = (z[i-1]*i)%mod;
			     z2 = new long[(int)N+1];
				z2[0] = z2[1] = 1;
			    for (int i = 2; i <= N; i++)
			        z2[i] = z2[(int)(mod % i)] * (mod - mod / i) % mod;
			    
			    
			    z1[0] = z1[1] = 1;
			    
			    for (int i = 2; i <= N; i++)
			        z1[i] = (z2[i] * z1[i - 1]) % mod;
			}
	    	  long fac(long n) {
	    		  return z[(int)n];
	    	  }
	    	  long invrsNum(long n) {
	    		  return z2[(int)n];
	    	  }
	    	  long invrsFac(long n) {
	    		  return invrsFac((int)n);
	    	  }
	    	  long ncr(long N, long R, long mod)
	    	  {		if(R<0 || R>N ) return 0;
	    		    long ans = ((z[(int)N] * z1[(int)R])
	    		              % mod * z1[(int)(N - R)])
	    		             % mod;
	    		    return ans;
	    		}
	      }
	      static class DisjointUnionSets {
			    int[] rank, parent;
			    int n;
			  
			    public DisjointUnionSets(int n)
			    {
			        rank = new int[n];
			        parent = new int[n];
			        this.n = n;
			        makeSet();
			    }
			  
			    void makeSet()
			    {
			        for (int i = 0; i < n; i++) {
			          
			            parent[i] = i;
			        }
			    }
			  
			    int find(int x)
			    {
			        if (parent[x] != x) {
			        
			            parent[x] = find(parent[x]);
			  
			        }
			  
			        return parent[x];
			    }
			  
			    void union(int x, int y)
			    {
			        int xRoot = find(x), yRoot = find(y);
			  
			        if (xRoot == yRoot)
			            return;
			  
			        if (rank[xRoot] < rank[yRoot])
			  
			            parent[xRoot] = yRoot;
			  
			        else if (rank[yRoot] < rank[xRoot])
			  
			            parent[yRoot] = xRoot;
			  
			        else
			        {
			            parent[yRoot] = xRoot;
			  
			            rank[xRoot] = rank[xRoot] + 1;
			        }
			    }
			}
	      static int[] KMP(String str) {
	    	  int n = str.length();
	    	  int[] kmp = new int[n];
	    	  for(int i = 1 ; i<n ; i++) {
	    		  int j = kmp[i-1];
	    		  while(j>0 && str.charAt(i) != str.charAt(j)) {
	    			  j = kmp[j-1];
	    		  }
	    		  if(str.charAt(i) == str.charAt(j)) j++;
	    		  kmp[i] = j;
	    	  }
	    	  
	    	  return kmp;
	      }
	      
	      
/************************************************ Query **************************************************************************************/	  
	 
/***************************************** 		Sparse Table	********************************************************/
	      static class SparseTable{
	    		
	    		private long[][] st;
	    		
	    		SparseTable(long[] arr){
	    			int n = arr.length;
	    			st = new long[n][25];
	    			log = new int[n+2];
	    			build_log(n+1);
	    			build(arr);
	    		}
	    		
	    		private void build(long[] arr) {
	    			int n = arr.length;
	    			
	    			for(int i = n-1 ; i>=0 ; i--) {
	    				for(int j = 0 ; j<25 ; j++) {
	    					int r = i + (1<<j)-1;
	    					if(r>=n) break;
	    					if(j == 0 ) st[i][j] = arr[i];
	    					else st[i][j] = Math.min(st[i][j-1] , st[ i + ( 1 << (j-1) ) ][ j-1 ] );
	    				}
	    			}
	    		}
	    		public long gcd(long a  ,long b) {
	    			if(a == 0) return b;
	    			return gcd(b%a , a);
	    		}
	    		public long query(int l ,int r) {
	    			int w = r-l+1;
	    			int power = log[w];
	    			return Math.min(st[l][power],st[r - (1<<power) + 1][power]);
	    		}
	    		private int[] log;
	    		void build_log(int n) {
	    			log[1] = 0;
	    			for(int i = 2 ; i<=n ; i++) {
	    				log[i] = 1 + log[i/2];
	    			}
	    		}
	    	}
	      
	      
/********************************************************	Segement Tree	*****************************************************/
/**
	 	 static class SegmentTree{
			 long[] tree;
			 long[] arr;
			 int n;
			 SegmentTree(long[] arr){
				 this.n = arr.length;
				 tree = new long[4*n+1];
				 this.arr = arr;
				 buildTree(0, n-1, 1);
			 }
			 
			 
			  void buildTree(int s ,int e  ,int index ) {
					if(s == e) {
						tree[index] = arr[s];
						return;
					}
				
					int mid = (s+e)/2;
					
					buildTree( s,  mid, 2*index);
					buildTree( mid+1, e, 2*index+1);
					
					tree[index] = Math.min(tree[2*index] , tree[2*index+1]);
				}
			  
			 long query(int si ,int ei) {
				 return query(0 ,n-1 , si ,ei , 1   );
			 }
			 private long query( int ss ,int se ,int qs , int qe,int index) {
					
					if(ss>=qs && se<=qe) return tree[index];
					
					if(qe<ss || se<qs) return (long)(1e17);
					
					int mid = (ss + se)/2;
					long left = query( ss , mid , qs ,qe , 2*index);
					long right= query(mid + 1 , se , qs ,qe , 2*index+1);
					return Math.min(left, right);
				}
			 public void update(int index , int val) {
				 arr[index] = val;
				 for(long e:arr) System.out.print(e+" ");
				 update(index , 0 , n-1 , 1);
			 }
			 private void update(int id ,int si , int ei , int index) {
				 if(id < si || id>ei) return;
				 if(si == ei ) { 
					 tree[index] = arr[id];
					 return;
				 }
				 if(si > ei) return;
				 int mid = (ei + si)/2;
					
					update( id,  si, mid , 2*index);
					update( id , mid+1, ei , 2*index+1);
					
					tree[index] = Math.min(tree[2*index] ,tree[2*index+1]);
			 }
			  
		 }
		 */

/* ***************************************************************************************************************************************************/	 
	 
	      static Reader sc = new Reader();
	 static StringBuilder sb = new StringBuilder();
	 public static void main(String args[]) throws IOException {
	
		 int tc = 1;
		  tc = sc.nextInt();
		 for(int i = 1 ; i<=tc ; i++) {

//			 sb.append("Case #" + i + ": "  );	// During KickStart && HackerCup
			 TEST_CASE();
			 
		 }
		 System.out.println(sb);

	 }
	static void TEST_CASE() {
		long n  = sc.nextInt() , m = sc.nextInt() , k = sc.nextInt()-1;
		if( k <= 0) {
			sb.append("NO\n");
			return;
		}
		long min = n-1;
		long max = ((n)*(n-1))/2;
		if(m>max || m<min) {
			sb.append("NO\n");
			return;
		}
		if(n == 1) {
			sb.append("YES\n");
			return;
		}
		if(m == max && k>1) {
//			System.out.println("HEllo");
			sb.append("YES\n");
			return;
		}
		if(k>2) {
			sb.append("YES\n");
			return;
		}
		sb.append("NO\n");
	}
}



/*******************************************************************************************************************************************************/

/**

 */






