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.*;

public class B {
    static StringBuilder sb;
    static long fact[];
    static int mod = (int) (1e9 + 7);
    static int[] arr = { 0, 1, 11, 111, 1111, 11111, 111111, 1111111, 11111111, 111111111, 1111111111 };

    static void solve(long n, long m, long k) {
        if (m < n - 1) {
            // System.out.println("1");
            sb.append("NO\n");
            return;
        }

        // System.out.println(n * (n - 1) / 2);

        if (m >= n - 1 && m < n * (n - 1) / 2 && k - 1 > 2) {
            sb.append("YES\n");
            return;
        }

        if (m == n * (n - 1) / 2 && k - 1 > 1) {
            sb.append("YES\n");
            return;
        }

        // System.out.println("2");

        sb.append("NO\n");

    }

    public static void main(String[] args) {
        sb = new StringBuilder();
        int test = i();
        while (test-- > 0) {
            long n = l(), m = l(), k = l();
            solve(n, m, k);
        }
        System.out.println(sb);

    }

    /*
     * fact=new long[(int)1e6+10]; fact[0]=fact[1]=1; for(int i=2;i<fact.length;i++)
     * { fact[i]=((long)(i%mod)1L(long)(fact[i-1]%mod))%mod; }
     */
    // **************NCR%P******************

    static long p(long x, long y)// POWER FXN //
    {
        if (y == 0)
            return 1;

        long res = 1;
        while (y > 0) {
            if (y % 2 == 1) {
                res = (res * x) % mod;
                y--;
            }

            x = (x * x) % mod;
            y = y / 2;

        }
        return res;
    }

    static long ncr(int n, int r) {
        if (r > n)
            return (long) 0;

        long res = fact[n] % mod;
        // System.out.println(res);
        res = ((long) (res % mod) * (long) (p(fact[r], mod - 2) % mod)) % mod;
        res = ((long) (res % mod) * (long) (p(fact[n - r], mod - 2) % mod)) % mod;
        // System.out.println(res);
        return res;

    }

    // **************END******************

    // *************Disjoint set
    // union*********//

    // ***************PRIME FACTORIZE
    // ***********************************//
    static TreeMap<Integer, Integer> prime(long n) {
        TreeMap<Integer, Integer> h = new TreeMap<>();
        long num = n;
        for (int i = 2; i <= Math.sqrt(num); i++) {
            if (n % i == 0) {
                int nt = 0;
                while (n % i == 0) {
                    n = n / i;
                    nt++;
                }
                h.put(i, nt);
            }
        }
        if (n != 1)
            h.put((int) n, 1);
        return h;

    }

    // *****CLASS PAIR
    // *************************************************
    static class Pair implements Comparable<Pair> {
        int x;
        long y;

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

        public int compareTo(Pair o) {
            return (int) (this.y - o.y);

        }

    }
    // *****CLASS PAIR
    // ***************************************************

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (numChars == -1)
                throw new InputMismatchException();
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        public int Int() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public String String() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        public boolean isSpaceChar(int c) {
            if (filter != null)
                return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public String next() {
            return String();
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);
        }
    }

    static class OutputWriter {
        private final PrintWriter writer;

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void print(Object... objects) {
            for (int i = 0; i < objects.length; i++) {
                if (i != 0)
                    writer.print(' ');
                writer.print(objects[i]);
            }
        }

        public void printLine(Object... objects) {
            print(objects);
            writer.println();
        }

        public void close() {
            writer.close();
        }

        public void flush() {
            writer.flush();
        }
    }

    static InputReader in = new InputReader(System.in);
    static OutputWriter out = new OutputWriter(System.out);

    public static long[] sortlong(long[] a2) {
        int n = a2.length;
        ArrayList<Long> l = new ArrayList<>();
        for (long i : a2)
            l.add(i);
        Collections.sort(l);
        for (int i = 0; i < l.size(); i++)
            a2[i] = l.get(i);
        return a2;
    }

    public static int[] sortint(int[] a2) {
        int n = a2.length;
        ArrayList<Integer> l = new ArrayList<>();
        for (int i : a2)
            l.add(i);
        Collections.sort(l);
        for (int i = 0; i < l.size(); i++)
            a2[i] = l.get(i);
        return a2;
    }

    public static long pow(long x, long y) {
        long res = 1;
        while (y > 0) {
            if (y % 2 != 0) {
                res = (res * x);// % modulus;
                y--;

            }
            x = (x * x);// % modulus;
            y = y / 2;
        }
        return res;
    }

    // GCD___+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
    public static long gcd(long x, long y) {
        if (x == 0)
            return y;
        else
            return gcd(y % x, x);
    }
    // ******LOWEST COMMON MULTIPLE
    // *********************************************

    public static long lcm(long x, long y) {
        return (x * (y / gcd(x, y)));
    }

    // INPUT
    // PATTERN********************************************************
    public static int i() {
        return in.Int();
    }

    public static long l() {
        String s = in.String();
        return Long.parseLong(s);
    }

    public static String s() {
        return in.String();
    }

    public static int[] readArray(int n) {
        int A[] = new int[n];
        for (int i = 0; i < n; i++) {
            A[i] = i();
        }
        return A;
    }

    public static long[] readArray(long n) {
        long A[] = new long[(int) n];
        for (int i = 0; i < n; i++) {
            A[i] = l();
        }
        return A;
    }

}