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.
						/*
						ID: abdelra29
	LANG: JAVA
	PROG: zerosum
						*/
							/*
							TO LEARN
					
							2-euler tour
						
							*/
							/*
							TO SOLVE 
							*/
							/*
							bit manipulation shit
							1-Computer Systems: A Programmer's Perspective
							2-hacker's delight
							*/
							/*
							TO WATCH
							
							*/
							            import java.util.*;
									    import java.math.*;
									    import java.io.*; 
									    import java.text.DecimalFormat;
									    import java.util.stream.Collectors;


									       public class A{
							            static FastScanner scan=new FastScanner();
										     public static PrintWriter out = new PrintWriter (new BufferedOutputStream(System.out));

    static void remove(Map<Integer,Integer>map,int x)
    {
    	if(map.get(x)==1)
    		map.remove(x);
    	else map.put(x,map.get(x)-1);
    }
    static long count[];
    static LinkedList<Integer>edges[];
    static void dfs1(int x,int p)
    {
    	count[x]=1;
    	for(int v:edges[x])
    	{
    		if(v!=p)
    		{
    			depth[v]=depth[x]+1;
    			dfs1(v,x);
    			count[x]+=count[v];

    		}
    	}
    }
    static long depth[];
    static long res[]; 
    static int n;
    static void dfs2(int x,int p)
    {
    	for(int v:edges[x])
    	{
    		if(p!=v)
    		{
    			//if(v==2)
    			//	out.println(res[x]);
    			res[v]=res[x]-count[v]+(n-count[v]);
    			dfs2(v,x);
    		}
    	}
    }

			public static void main(String[] args)  throws Exception 
							      {
							 /*
							 very important tips 
							 1-just fucking think backwards once in your shitty life
							 2-consider brute forcing and finding some patterns and observations
							 3-when you're in contest don't get out because you think there is no enough time
							 4-don't get stuck on one approach 
							 */
						   
//			scan=new FastScanner("D:\\usaco test data\\WW.txt");
//			out = new PrintWriter("D:\\usaco test data\\WWW.txt");

						
									 							 /*
									 READING 
							
									 3-Introduction to DP with Bit-masking codeforces
									 4-Bit Manipulation hacker-earth
									 5-read more about mobious and inclusion-exclusion 
				 				     6-read more about Fermat little theorem
									 */
									 /*
									   -if the two persons are on the same line then it's not possible because that means the shortest path is either abs(x2-x1) or abs(y2-y1) and Manhattan will be abs(x2-x1)+abs(y2-y1) and it's obvious that it will be at least equal 
									   -if the first person is on vertical and second is on horizontal then it's not possible  
									 */

				 			
								//	System.out.println(1L<<62L);      
int tt=1;
								tt=scan.nextInt();
								int T=1;
								 outer:while(tt-->0)
								    {
								    	 int n=scan.nextInt(),m=scan.nextInt(),k=scan.nextInt()-1;
								    	/*if(tt==99373-547){
								    		out.println(k);
								    	}//2 0 2*/
								    	if(n==1&&m==0&&k>=1)
								    	{
								    		out.println("YES");
								    		continue outer;
								    	}
								    	if(m<n-1)
								    	{
								    		out.println("NO");
								    		continue outer;
								    	}

								    	 if(m>(n*(n-1))/2)
								    	{
								    	//	out.println(n*(n-1)/2);
								    		out.println("NO");
								    		continue outer;
								    	}
								    	//out.println("F");
								    	/*if(m==0&&k>0)
								    	{
								    		out.println("YES");
								    		continue outer;
								    	}*/
								 
								    	 if(k>2)
								    	 {
								    	 	out.println("YES");
								    	 	continue outer;
								    	 }
								    	 int need=n-1,rem=m-(n-1);
								    	 if(rem>=need*(need-1)/2)
								    	 {
								    	 	out.println("FUCK");
								    	 	if(k>=2)
								    	 	out.println("YES");
								    	 else out.println("NO");
								    	 }
								    	 else{
								    	// out.println("FUCK"); 
								    	 	//di 2
								    	 	if(k>2)
								    	 	out.println("YES");
								    	 else 
								    	 	out.println("NO");

}




								    	


  			   	
	 }							
	
        

			out.close();
						}
						
						

						static class special implements Comparable<special>{
						int cnt,idx;
						String s;
						public special(int cnt,int idx,String s)
						{
							this.cnt=cnt;
							this.idx=idx;
							this.s=s;
						}

							 @Override
									            public int hashCode() {
									                return (int)42;
									            }
							  @Override
									            public boolean equals(Object o){
									            //	System.out.println("FUCK");
									                if (o == this) return true;
									                if (o.getClass() != getClass()) return false;
									                special t = (special)o;
									                return t.cnt == cnt && t.idx == idx;
									            }
									            public int compareTo(special o1)
									            {
									            	if(o1.cnt==cnt)
									            	{
									            		return o1.idx-idx;
									            	}
									            	return o1.cnt-cnt;
									            }
						}
			
									   
									     static long binexp(long a,long n)
									    {
									        if(n==0)
									            return 1;
									        long res=binexp(a,n/2);
									        if(n%2==1)
									            return res*res*a;
									        else 
									            return res*res;
									    }
									     
									    static long powMod(long base, long exp, long mod) {
									           if (base == 0 || base == 1) return base;
									           if (exp == 0) return 1;
									           if (exp == 1) return (base % mod+mod)%mod;
									           long R = (powMod(base, exp/2, mod) % mod+mod)%mod;
									           R *= R;
									           R %= mod;
									           if ((exp & 1) == 1) {
									               return (base * R % mod+mod)%mod;
									           }
									           else return (R %mod+mod)%mod;
									       }
									    static double dis(double x1,double y1,double x2,double y2)
									    {
									        return Math.sqrt((x1-x2)*(x1-x2)+(y1-y2)*(y1-y2));
									    }
									    static long mod(long x,long y)
									        {
									            if(x<0)
									                x=x+(-x/y+1)*y;
									            return x%y;
									        }
									     public static  long pow(long b, long e) {
									                long r = 1;
									                while (e > 0) {
									                    if (e % 2 == 1) r = r * b ;
									                    b = b * b;
									                    e >>= 1;
									                }
									                return r;
									            }
									    private static void sort(int[] arr) {
									            List<Integer> list = new ArrayList<>();
									            for (int object : arr) list.add(object);
									            Collections.sort(list);
									        //Collections.reverse(list);
									            for (int i = 0; i < list.size(); ++i) arr[i] = list.get(i);
									        }
									    private static void sort2(long[] arr) {
									            List<Long> list = new ArrayList<>();
									            for (Long object : arr) list.add(object);
									            Collections.sort(list);
									        Collections.reverse(list);
									            for (int i = 0; i < list.size(); ++i) arr[i] = list.get(i);
									        }
									     static class FastScanner
							{
							    private int BS = 1 << 16;
							    private char NC = (char) 0;
							    private byte[] buf = new byte[BS];
							    private int bId = 0, size = 0;
							    private char c = NC;
							    private double cnt = 1;
							    private BufferedInputStream in;
							 
							    public FastScanner() {
							        in = new BufferedInputStream(System.in, BS);
							    }
							 
							    public FastScanner(String s) {
							        try {
							            in = new BufferedInputStream(new FileInputStream(new File(s)), BS);
							        } catch (Exception e) {
							            in = new BufferedInputStream(System.in, BS);
							        }
							    }
							 
							    private char getChar() {
							        while (bId == size) {
							            try {
							                size = in.read(buf);
							            } catch (Exception e) {
							                return NC;
							            }
							            if (size == -1) return NC;
							            bId = 0;
							        }
							        return (char) buf[bId++];
							    }
							 
							    public int nextInt() {
							        return (int) nextLong();
							    }
							 
							    public int[] nextInts(int N) {
							        int[] res = new int[N];
							        for (int i = 0; i < N; i++) {
							            res[i] = (int) nextLong();
							        }
							        return res;
							    }
							 
							    public long[] nextLongs(int N) {
							        long[] res = new long[N];
							        for (int i = 0; i < N; i++) {
							            res[i] = nextLong();
							        }
							        return res;
							    }
							 
							    public long nextLong() {
							        cnt = 1;
							        boolean neg = false;
							        if (c == NC) c = getChar();
							        for (; (c < '0' || c > '9'); c = getChar()) {
							            if (c == '-') neg = true;
							        }
							        long res = 0;
							        for (; c >= '0' && c <= '9'; c = getChar()) {
							            res = (res << 3) + (res << 1) + c - '0';
							            cnt *= 10;
							        }
							        return neg ? -res : res;
							    }
							 
							    public double nextDouble() {
							        double cur = nextLong();
							        return c != '.' ? cur : cur + nextLong() / cnt;
							    }
							 
							    public double[] nextDoubles(int N) {
							        double[] res = new double[N];
							        for (int i = 0; i < N; i++) {
							            res[i] = nextDouble();
							        }
							        return res;
							    }
							 
							    public String next() {
							        StringBuilder res = new StringBuilder();
							        while (c <= 32) c = getChar();
							        while (c > 32) {
							            res.append(c);
							            c = getChar();
							        }
							        return res.toString();
							    }
							 
							    public String nextLine() {
							        StringBuilder res = new StringBuilder();
							        while (c <= 32) c = getChar();
							        while (c != '\n') {
							            res.append(c);
							            c = getChar();
							        }
							        return res.toString();
							    }
							 
							    public boolean hasNext() {
							        if (c > 32) return true;
							        while (true) {
							            c = getChar();
							            if (c == NC) return false;
							            else if (c > 32) return true;
							        }
							    }
							}

									     static class Pair implements Comparable<Pair>{
									            public long x, y,z;
									            public Pair(long x1, long y1,long z1) {
									                x=x1;
									                y=y1;
									                z=z1;
									            }
									             public Pair(long x1, long y1) {
									                x=x1;
									                y=y1;
									    
									            }
									            
									            @Override
									            public int hashCode() {
									                return (int)(x + 31 * y);
									            }
									            public String toString() {
									                return x + " " + y+" "+z;
									            }
									            @Override
									            public boolean equals(Object o){
									                if (o == this) return true;
									                if (o.getClass() != getClass()) return false;
									                Pair t = (Pair)o;
									                return t.x == x && t.y == y&&t.z==z;
									            }
									    public int compareTo(Pair o)
									    {
									    								  	
									  if(x==o.x)
									  	return (int)(y-o.y);
									    	return (int)(x-o.x);
									     
									        }
									     
									    }
									}
									
									    
									   

									     
