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.io.BufferedReader;
    import java.io.FileInputStream;
    import java.io.FileNotFoundException;
    import java.io.IOException;
    import java.io.InputStreamReader;
    import java.util.*;
import java.util.concurrent.LinkedBlockingDeque;

import javax.print.attribute.HashAttributeSet;
import javax.swing.JLabel;

import java.io.PrintStream;
            
                public class Solution {

                    public static boolean Local(){
                        try{ 
                            return System.getenv("LOCAL_SYS")!=null;
                        }catch(Exception e){
                            return false;
                        }
                    }   

                    public static boolean LOCAL;

                    static class FastScanner {

                            BufferedReader br;
                            StringTokenizer st ;

                            FastScanner(){
                                br =  new BufferedReader(new InputStreamReader(System.in));
                                st = new StringTokenizer("");
                            }

                            FastScanner(String file) {

                                try{
                                    br =  new BufferedReader(new InputStreamReader(new FileInputStream(file)));
                                    st = new StringTokenizer("");
                                }catch(FileNotFoundException e) {
                                    // TODO Auto-generated catch block
                                    System.out.println("file not found");
                                    e.printStackTrace();
                                }
                                
                            }
                            

                            String next() {
                                while (!st.hasMoreTokens())
                                    try {
                                        st = new StringTokenizer(br.readLine());
                                    } catch (IOException e) {
                                    }
                                return st.nextToken();
                            }

                            int nextInt() {
                                return Integer.parseInt(next());
                            }

                            long nextLong() {
                                return Long.parseLong(next());
                            }
                            String readLine() throws IOException{
                                return br.readLine();
                            }
                        }
                                            
                    static class Pair<T,X> {

                        T first;
                        X second;
                        
                        Pair(T first,X second){
                            this.first = first;
                            this.second = second;
                        }

                        @Override
                        public int hashCode(){
                            return Objects.hash(first,second);
                        }

                        @Override
                        public boolean equals(Object obj){
                            return obj.hashCode() == this.hashCode();
                        }

                    }

                
                static PrintStream debug = null;

                static long mod = (long)(Math.pow(10,9) + 7); 
                

                public static void main(String[] args) throws Exception {
                    
                    FastScanner s = new FastScanner();

                    LOCAL = Local();

                    
                    if(LOCAL){
                        s = new FastScanner("src/input.txt");
                        PrintStream o = new PrintStream("src/sampleout.txt");
                        debug = new PrintStream("src/debug.txt");
                        System.setOut(o);
                    }

                    long mod = 1000000007;
                
                    int tcr = s.nextInt();                  
                    
                    long fact[] = new long[200001];
                    
                    fact[0] = 1;

                    for(int i=1;i<fact.length;i++){
                        fact[i] = mulmod(fact[i],i,mod);
                    }

                    StringBuilder sb = new StringBuilder();

                    for(int tc=0;tc<tcr;tc++){
                        
                        long n = s.nextLong();

                        long m = s.nextLong();

                        long k = s.nextLong();

                        long all_edges = (n*(n-1))/2l;

                        if(m > all_edges){
                            sb.append("NO\n");
                            continue;
                        }

                        if(n==1l){
                            if(k>=1){
                                sb.append("YES\n");
                            }else{
                                sb.append("NO\n");
                            }
                            continue;
                        }

                        long max_dia = 1 + (all_edges - m);

                       // println(all_edges+" "+max_dia);

                        if(max_dia < k-1){
                            sb.append("YES\n");
                        }else{
                            sb.append("NO\n");
                        }
                    }


                    print(sb.toString());
                }

                
                

                public static List<long[]> prime_factors(long n){
            
                    List<long[]> list = new ArrayList<>();
                    
                    for(long i=2;i<=(Math.sqrt(n));i++){
            
                        if(n % i == 0){
                            
                            int cnt = 0;
                            
                            while( (n % i) == 0){
                                n = n/i;
                                cnt++;
                                
                            }
            
                            list.add(new long[]{i,cnt});
                        }
                    }

            
                    if(n!=1){
                        list.add(new long[]{n,1l});
                    }
            
                    return list;
            
                }

                public static boolean check(int arr[]){
                    for(int i=1;i<arr.length;i++){
                        if(arr[i] < arr[i-1]){
                            return false;
                        }
                    }
                    return true;
                }

            
                public static boolean inRange(int r1,int r2,int val){
                    return ((val >= r1) && (val <= r2));
                }

                static int len(long num){
                    return Long.toString(num).length();
                }

                static long mulmod(long a, long b,long mod)
                {
                    long ans = 0l;
                    
                    while(b > 0){
                        long curr = (b & 1l);
                        if(curr == 1l){
                            ans = ((ans % mod) + a) % mod;
                        }
                        
                        a = (a + a) % mod;

                        b = b >> 1;
                    }

                    return ans;
                }


                public static void dbg(PrintStream ps,Object... o) throws Exception{
                    if(ps == null){
                        return;
                    }
                    Debug.dbg(ps,o);
                }

                public static long modpow(long num,long pow,long mod){

                    long val = num;
                    long ans = 1l;

                    while(pow > 0l){
                        
                        long bit = pow & 1l;

                        if(bit == 1){
                            ans = (ans * (val%mod))%mod;
                        }

                        val = (val * val) % mod;
                        pow = pow >> 1;
                    }

                    return ans;

                }

                public static char get(int n){
                    return (char)('a' + n);
                }

                public static long[] sort(long arr[]){
                    List<Long> list = new ArrayList<>();
                    for(long n : arr){list.add(n);}
                    Collections.sort(list);
                    for(int i=0;i<arr.length;i++){
                        arr[i] = list.get(i);
                    }
                    return arr;
                }

                public static int[] sort(int arr[]){
                    List<Integer> list = new ArrayList<>();
                    for(int n : arr){list.add(n);}
                    Collections.sort(list);
                    for(int i=0;i<arr.length;i++){
                        arr[i] = list.get(i);
                    }
                    return arr;
                }

                // return the (index + 1)
                // where index is the pos of just smaller element
                // i.e count of elemets strictly less than num
                public static int justSmaller(long arr[],long num){
                    //  System.out.println(num+"@");
                    int st = 0;
                    int e = arr.length - 1;
            
                    int ans = -1;
            
                    while(st <= e){
            
                        int mid = (st + e)/2;
            
                        if(arr[mid] >= num){
                            e = mid - 1;
                        }else{
                            ans = mid;
                            st = mid + 1;
                        }
            
                    }
            
            
                    return ans + 1;
            
                }
                public static int justSmaller(int arr[],int num){
                    //  System.out.println(num+"@");
                    int st = 0;
                    int e = arr.length - 1;
            
                    int ans = -1;
            
                    while(st <= e){
            
                        int mid = (st + e)/2;
            
                        if(arr[mid] >= num){
                            e = mid - 1;
                        }else{
                            ans = mid;
                            st = mid + 1;
                        }
            
                    }
            
            
                    return ans + 1;
            
                }
                
                //return (index of just greater element)
                //count of elements smaller than or equal to num

                public static int justGreater(long arr[],long num){
                    int st = 0;
                    int e = arr.length - 1;
            
                    int ans = arr.length;
            
                    while(st <= e){
                        
                        int mid = (st + e)/2;
            
                        if(arr[mid] <= num){
                            st = mid + 1;
                        }else{
                            ans = mid;
                            e = mid - 1;
                        }
                    }
            
                    return ans;
            
                }

                public static int justGreater(int arr[],int num){
                    int st = 0;
                    int e = arr.length - 1;
            
                    int ans = arr.length;
            
                    while(st <= e){
                        
                        int mid = (st + e)/2;
            
                        if(arr[mid] <= num){
                            st = mid + 1;
                        }else{
                            ans = mid;
                            e = mid - 1;
                        }
                    }
            
                    return ans;
            
                }
            
                

                public static void println(Object obj){
                    System.out.println(obj.toString());
                }

                public static void print(Object obj){
                    System.out.print(obj.toString());
                }

                public static int gcd(int a,int b){
                    if(b == 0){return a;}
                    return gcd(b,a%b);
                }

                public static long gcd(long a,long b){
                    if(b == 0l){
                        return a;
                    }

                    return gcd(b,a%b);
                }

                public static int find(int parent[],int v){
                    if(parent[v] == v){
                        return v;
                    }
                    
                    return parent[v] = find(parent, parent[v]);
                }

            

                public static List<Integer> sieve(){
                
                        List<Integer> prime = new ArrayList<>();

                        int arr[] = new int[100001];

                    Arrays.fill(arr,1);

                    arr[1] = 0;
                    arr[2] = 1;

                    for(int i=2;i<=100000;i++){
                        
                        if(arr[i] == 1){
                            
                            prime.add(i);

                            for(long j = (i*1l*i);j<100001;j+=i){
                                arr[(int)j] = 0;
                            }
                        }
                    }

                    return prime;
                }

                static boolean isPower(long n,long a){
                    
                    long log = (long)(Math.log(n)/Math.log(a));

                    long power = (long)Math.pow(a,log);

                    if(power == n){return true;}

                    return false;
                }


                private static int mergeAndCount(int[] arr, int l,int m, int r)
                {

                    // Left subarray
                    int[] left =  Arrays.copyOfRange(arr, l, m + 1);

                    // Right subarray
                    int[] right = Arrays.copyOfRange(arr, m + 1, r + 1);

                    int i = 0, j = 0, k = l, swaps = 0;

                    while (i < left.length && j < right.length) {
                        if (left[i] <= right[j])
                            arr[k++] = left[i++];
                        else {
                            arr[k++] = right[j++];
                            swaps += (m + 1) - (l + i);
                        }
                    }
                    while (i < left.length)
                        arr[k++] = left[i++];
                    while (j < right.length)
                        arr[k++] = right[j++];
                    return swaps;
                }

                // Merge sort function
                private static int mergeSortAndCount(int[] arr, int l,int r)
                {

                    // Keeps track of the inversion count at a
                    // particular node of the recursion tree
                    int count = 0;

                    if (l < r) {
                        int m = (l + r) / 2;

                        // Total inversion count = left subarray count
                        // + right subarray count + merge count

                        // Left subarray count
                        count += mergeSortAndCount(arr, l, m);

                        // Right subarray count
                        count += mergeSortAndCount(arr, m + 1, r);

                        // Merge count
                        count += mergeAndCount(arr, l, m, r);
                    }

                    return count;
                }

                static class Debug{
                    //change to System.getProperty("ONLINE_JUDGE")==null; for CodeForces
                    public static final boolean LOCAL = System.getProperty("ONLINE_JUDGE")==null;

                    

                    private static <T> String ts(T t) {
                        if(t==null) {
                            return "null";
                        }
                        try {
                            return ts((Iterable) t);
                        }catch(ClassCastException e) {
                            if(t instanceof int[]) {
                                String s = Arrays.toString((int[]) t);
                                return "{"+s.substring(1, s.length()-1)+"}\n";
                            }else if(t instanceof long[]) {
                                String s = Arrays.toString((long[]) t);
                                return "{"+s.substring(1, s.length()-1)+"}\n";
                            }else if(t instanceof char[]) {
                                String s = Arrays.toString((char[]) t);
                                return "{"+s.substring(1, s.length()-1)+"}\n";
                            }else if(t instanceof double[]) {
                                String s = Arrays.toString((double[]) t);
                                return "{"+s.substring(1, s.length()-1)+"}\n";
                            }else if(t instanceof boolean[]) {
                                String s = Arrays.toString((boolean[]) t);
                                return "{"+s.substring(1, s.length()-1)+"}\n";
                            }
                            try {
                                return ts((Object[]) t);
                            }catch(ClassCastException e1) {
                                return t.toString();
                            }
                        }
                    }
                    private static <T> String ts(T[] arr) {
                        StringBuilder ret = new StringBuilder();
                        ret.append("{");
                        boolean first = true;
                        for(T t: arr) {
                            if(!first) {
                                ret.append(", ");
                            }
                            first = false;
                            ret.append(ts(t));
                        }
                        ret.append("}");
                        return ret.toString();
                    }
                    private static <T> String ts(Iterable<T> iter) {
                        StringBuilder ret = new StringBuilder();
                        ret.append("{");
                        boolean first = true;
                        for(T t: iter) {
                            if(!first) {
                                ret.append(", ");
                            }
                            first = false;
                            ret.append(ts(t));
                        }
                        ret.append("}");
                        return ret.toString();
                    }
                    public static void dbg(PrintStream ps,Object... o) throws Exception {
                        if(LOCAL) {
                            System.setErr(ps);
                            System.err.print("Line #"+Thread.currentThread().getStackTrace()[2].getLineNumber()+": [");
                            for(int i = 0; i<o.length; i++) {
                                if(i!=0) {
                                    System.err.print(", ");
                                }
                                System.err.print(ts(o[i]));
                            }
                            System.err.println("]");
                        }
                    }
                }

        }


        