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.
//package codeforces;

import java.io.*;
import java.util.*;

public class ProblemB {
    private final static FastScanner scanner = new FastScanner();

    public static void main(String[] args) throws IOException {
        int n = scanner.nextInt();
        for (int i = 0; i < n; i++) {
            solve();
        }
//        solve();
    }

    public static void solve() {
        long n = scanner.nextLong();
        long m = scanner.nextLong();
        long k = scanner.nextLong();
        if (k <= 1) {
            System.out.println("NO");
            return;
        }
        if (k == 2) {
            if (m == 0 && n == 1) {
                System.out.println("YES");
            } else {
                System.out.println("NO");
            }
            return;
        }
        if((m == 0 && n == 1)){
            System.out.println("YES");
            return;
        }
        if(m >= n - 1 && m < sumOfNNaturalNumbers(n - 1) && k > 3){
            System.out.println("YES");
        }else if(m == sumOfNNaturalNumbers(n - 1)){
            System.out.println("YES");
        }else {
            System.out.println("NO");
        }
    }

    public static long getManhattanDistance(long x1, long y1, long x2, long y2) {
        return Math.abs(x1 - x2) + Math.abs(y1 - y2);
    }

    public static long lcm(long number1, long number2) {
        if (number1 == 0 || number2 == 0) {
            return 0;
        }
        long absNumber1 = Math.abs(number1);
        long absNumber2 = Math.abs(number2);
        long absHigherNumber = Math.max(absNumber1, absNumber2);
        long absLowerNumber = Math.min(absNumber1, absNumber2);
        long lcm = absHigherNumber;
        while (lcm % absLowerNumber != 0) {
            lcm += absHigherNumber;
        }
        return lcm;
    }

    static void swap(int[] arr, int l, int r) {
        int temp = arr[l];
        arr[l] = arr[r];
        arr[r] = temp;
    }

    static void swap(long[] arr, int l, int r) {
        long temp = arr[l];
        arr[l] = arr[r];
        arr[r] = temp;
    }

    private static int getTickSize(char[][] mat, int i, int j) {
        if (i < 0 || j < 0 || i >= mat.length || j >= mat[0].length || mat[i][j] == '.') return 0;
        mat[i][j] = '.';
        return Math.min(getTickSize(mat, i - 1, j - 1), getTickSize(mat, i - 1, j + 1));
    }

    private static Boolean isSquare(long x) {
        long y = (long) Math.sqrt(x);
        return y * y == x;
    }

    private static int getMax(int[] arr) {
        int[] copy = Arrays.copyOf(arr, arr.length);
        Arrays.sort(copy);
        return copy[arr.length - 1];
    }

    private static double customLog(double logNumber, double base) {
        return Math.log(logNumber) / Math.log(base);
    }


    static int checkSim(String n1, String n2, int i, int j) {
        if (i >= n1.length() || j >= n2.length()) return 0;
        if (n1.charAt(i) == n2.charAt(j)) return 1 + checkSim(n1, n2, i + 1, j + 1);
        return checkSim(n1, n2, i + 1, j);
    }

    static int computeXOR(int n) {
        if (n % 4 == 0)
            return n;
        if (n % 4 == 1)
            return 1;
        if (n % 4 == 2)
            return n + 1;
        return 0;
    }

    static boolean isPowerOfTwo(long n) {
        if (n == 0)
            return false;

        double v = Math.log(n) / Math.log(2);
        return (long) (Math.ceil(v)) == (long) (Math.floor(v));
    }

    static boolean isPrime(int n) {
        if (n <= 1)
            return false;

        else if (n == 2)
            return true;

        else if (n % 2 == 0)
            return false;

        for (int i = 3; i <= Math.sqrt(n); i += 2) {
            if (n % i == 0)
                return false;
        }
        return true;
    }

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

    static void print(int from, int to) {
        if (from <= to) {
            for (int i = from; i <= to; i++) {
                System.out.print(i + " ");
            }
        } else {
            System.out.print(from + " ");
            for (int i = 1; i <= to; i++) {
                System.out.print(i + " ");
            }
        }
    }

    static long moduloMultiplication(long a, long b, long mod) {
        long res = 0;
        a %= mod;
        while (b > 0) {
            if ((b & 1) > 0) {
                res = (res + a) % mod;
            }
            a = (2 * a) % mod;
            b >>= 1;
        }
        return res;
    }

    static long moduloPower(long x, long y, long p) {
        long res = 1L;
        x = x % p;
        while (y > 0) {
            if ((y & 1) > 0)
                res = (res * x) % p;

            y = y >> 1;
            x = (x * x) % p;
        }
        return res;
    }

    static int lowerBound(long a[], long x) { // x is the target value or key
        int l = -1, r = a.length;
        while (l + 1 < r) {
            int m = (l + r) >>> 1;
            if (a[m] >= x) r = m;
            else l = m;
        }
        return r;
    }

    static int upperBound(long a[], long x) {// x is the key or target value
        int l = -1, r = a.length;
        while (l + 1 < r) {
            int m = (l + r) >>> 1L;
            if (a[m] <= x) l = m;
            else r = m;
        }
        return l + 1;
    }

    static long upperBound(long[] arr, int start, int end, long k) {
        int N = end;
        while (start < end) {
            int mid = start + (end - start) / 2;
            if (k >= arr[mid]) {
                start = mid + 1;
            } else {
                end = mid;
            }
        }
        if (start < N && arr[start] <= k) {
            start++;
        }
        return start;
    }

    static long lowerBound(long[] arr, int start, int end, long k) {
        int N = end;
        while (start < end) {
            int mid = start + (end - start) / 2;
            if (k <= arr[mid]) {
                end = mid;
            } else {
                start = mid + 1;
            }
        }
        if (start < N && arr[start] < k) {
            start++;
        }
        return start;
    }

    static int getDistance(int x1, int y1, int x2, int y2) {
        return Math.abs(x1 - x2) + Math.abs(y1 - y2);
    }

    static int sumOfNNaturalNumbers(int n) {
        return (n * (n + 1)) / 2;
    }

    static long sumOfNNaturalNumbers(long n) {
        return (n * (n + 1)) / 2;
    }

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


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

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

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

        int[] readArray(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++) a[i] = nextInt();
            return a;
        }

        long nextLong() {
            return Long.parseLong(next());
        }
    }
}