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.io.*;
import java.math.*;
import java.lang.*;

public class b {
    
    static int mod = 1000000007;

    public static class Reader {
        final private int BUFFER_SIZE = 1 << 16;
        private DataInputStream din;
        private byte[] buffer;
        private int bufferPointer, bytesRead;
 
        public Reader()
        {
            din = new DataInputStream(System.in);
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }
 
        public Reader(String file_name) throws IOException
        {
            din = new DataInputStream(
                new FileInputStream(file_name));
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }
 
        public String readLine() throws IOException
        {
            byte[] buf = new byte[64]; // line length
            int cnt = 0, c;
            while ((c = read()) != -1) {
                if (c == '\n') {
                    if (cnt != 0) {
                        break;
                    }
                    else {
                        continue;
                    }
                }
                buf[cnt++] = (byte)c;
            }
            return new String(buf, 0, cnt);
        }
 
        public int nextInt() throws IOException
        {
            int ret = 0;
            byte c = read();
            while (c <= ' ') {
                c = read();
            }
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');
 
            if (neg)
                return -ret;
            return ret;
        }
 
        public long nextLong() throws IOException
        {
            long ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');
            if (neg)
                return -ret;
            return ret;
        }
 
        public double nextDouble() throws IOException
        {
            double ret = 0, div = 1;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
 
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');
 
            if (c == '.') {
                while ((c = read()) >= '0' && c <= '9') {
                    ret += (c - '0') / (div *= 10);
                }
            }
 
            if (neg)
                return -ret;
            return ret;
        }
 
        private void fillBuffer() throws IOException
        {
            bytesRead = din.read(buffer, bufferPointer = 0,
                                 BUFFER_SIZE);
            if (bytesRead == -1)
                buffer[0] = -1;
        }
 
        private byte read() throws IOException
        {
            if (bufferPointer == bytesRead)
                fillBuffer();
            return buffer[bufferPointer++];
        }
 
        public void close() throws IOException
        {
            if (din == null)
                return;
            din.close();
        }
    }

    public static void main(String[] args) throws Exception {
        Reader scn = new Reader();
        PrintWriter pw = new PrintWriter(System.out);
        int t = scn.nextInt();
        outer : while(t-->0){
            long n = scn.nextLong();
            long m = scn.nextLong();
            long k = scn.nextLong();
            if(k == 0L || k == 1L){
                pw.println("NO");
                continue outer;
            }
            long maxEdge = (n*(n-1L))/2;
            if((m < n - 1L) || m > maxEdge){
                pw.println("NO");
                continue outer;
            }
            if(m == maxEdge){
                if(m == 0){
                    if(k >= 2){
                        pw.println("YES");
                    }else{
                        pw.println("NO");
                    }
                }else{
                    if(k >= 3){
                        pw.println("YES");
                    }else{
                        pw.println("NO");
                    }
                }
            }else{
                if(k >= 4){
                    pw.println("YES");
                }else{
                    pw.println("NO");
                }
            }
        }
        pw.close();
    }

    public static class Pair{
        long x;
        long y;

        Pair(long x, long y){
            this.x = x;
            this.y = y;
        }
    }

    private static void sort(int[] arr) {
        List<Integer> list = new ArrayList<>();
        for (int i=0; i<arr.length; i++){
            list.add(arr[i]);
        }
        Collections.sort(list); // collections.sort uses nlogn in backend
        for (int i = 0; i < arr.length; i++){
            arr[i] = list.get(i);
        }
    }

    private static void sort(long[] arr) {
        List<Long> list = new ArrayList<>();
        for(int i=0; i<arr.length; i++){
            list.add(arr[i]);
        }
        Collections.sort(list); // collections.sort uses nlogn in backend
        for (int i = 0; i < arr.length; i++){
            arr[i] = list.get(i);
        }
    }

    private static int lowerBound(int[] arr, int x){
        int n = arr.length, si = 0, ei = n - 1;
        while(si <= ei){
            int mid = si + (ei - si)/2;
            if(arr[mid] == x){
                if(mid-1 >= 0 && arr[mid-1] == arr[mid]){
                    ei = mid-1;
                }else{
                    return mid;
                }
            }else if(arr[mid] > x){
                ei = mid - 1; 
            }else{
                si = mid+1;
            }
        }
        return si; 
    }

    private static int upperBound(int[] arr, int x){
        int n = arr.length, si = 0, ei = n - 1;
        while(si <= ei){
            int mid = si + (ei - si)/2;
            if(arr[mid] == x){
                if(mid+1 < n && arr[mid+1] == arr[mid]){
                    si = mid+1;
                }else{
                    return mid + 1;
                }
            }else if(arr[mid] > x){
                ei = mid - 1; 
            }else{
                si = mid+1;
            }
        }
        return si; 
    }

    private static int upperBound(ArrayList<Integer> list, int x){
        int n = list.size(), si = 0, ei = n - 1;
        while(si <= ei){
            int mid = si + (ei - si)/2;
            if(list.get(mid) == x){
                if(mid+1 < n && list.get(mid+1) == list.get(mid)){
                    si = mid+1;
                }else{
                    return mid + 1;
                }
            }else if(list.get(mid) > x){
                ei = mid - 1; 
            }else{
                si = mid+1;
            }
        }
        return si; 
    }

    // (x^y)%p in O(logy)
    private static long power(long x, long y){
        long res = 1; 
        x = x % mod;
        while(y > 0){
            if ((y & 1) == 1){
                res = (res * x) % mod;
            }
            y = y >> 1; 
            x = (x * x) % mod;
        }
        return res;
    }

    public static boolean nextPermutation(int[] arr) {
        if(arr == null || arr.length <= 1){
            return false;
        }
        
        int last = arr.length-2;
        while(last >= 0){
            if(arr[last] < arr[last+1]){
                break;
            }
            last--;
        }

        if (last < 0){
              return false;
        }
        
        if(last >= 0){
            int nextGreater = arr.length-1;
            for(int i=arr.length-1; i>last; i--){
                if(arr[i] > arr[last]){
                    nextGreater = i;
                    break;
                }
            }
            swap(arr, last, nextGreater);
        }
        
        reverse(arr, last+1, arr.length-1);
        return true;
    }
    
    private static void swap(int[] arr, int i, int j){
        int temp = arr[i];
        arr[i] = arr[j];
        arr[j] = temp;
    }
    
    private static void reverse(int[] arr, int i, int j){
        while(i < j){
            swap(arr, i++, j--);
        }
    }

    // TC- O(logmax(a,b))
    private static int gcd(int a, int b) {
        if(a == 0){
            return b;
        }
        return gcd(b%a, a);
    }

    private static long gcd(long a, long b) {
        if(a == 0L){
            return b;
        }
        return gcd(b%a, a);
    }

    private static long lcm(long a, long b) {
        return a / gcd(a, b) * b;
    }

    // TC- O(logmax(a,b))
    private static int lcm(int a, int b) {
        return a / gcd(a, b) * b;
    }

    private static long inv(long x){
        return power(x, mod - 2);
    }

    private static long summation(long n){
        return (n * (n + 1L)) >> 1;
    } 
}