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.IOException;
import java.io.InputStreamReader;
import java.util.*;
 
public class Solution{
static FastScanner sc = new FastScanner();
public static void solve() {
  int n=sc.nextInt(),m=sc.nextInt(),k=sc.nextInt();
  if (m==0) {
    if (n==1) {
      System.out.println("YES");
    }else
    System.out.println("NO");
    return;
  }
  if (n>m) {
    System.out.println("NO");
    return;
  }
  long k1=((long)(n)*(n-1))/2l;
  long m1=(long)m;
  if(m1>k1)
  {
    System.out.println("NO");
    return;
  }
  long z=k1%m1;
  if (z<k-2) {
    System.out.println("YES");
  }else
  System.out.println("NO");
  }
public static void main(String[] args) {
  int t = sc.nextInt();
  outer: for (int tt = 0; tt < t; tt++) {
    solve();
  }

}

////////////////////////////////////////////////////////////////////////////////////
////////////////////DO NOT READ AFTER THIS LINE //////////////////////////////////
////////////////////////////////////////////////////////////////////////////////////
static long modFact(int n, 
                       int p) 
    { 
        if (n >= p) 
            return 0; 
      
        long result = 1l; 
        for (int i = 3; i <= n; i++) 
            result = (result * i) % p; 
      
        return result; 
    } 
      
static boolean isPalindrom(char[] arr, int i, int j) {
  boolean ok = true;
  while (i <= j) {
    if (arr[i] != arr[j]) {
      ok = false;
      break;
    }
    i++;
    j--;
  }
  return ok;
}

static int max(int a, int b) {
  return Math.max(a, b);
}

static int min(int a, int b) {
  return Math.min(a, b);
}

static long max(long a, long b) {
  return Math.max(a, b);
}

static long min(long a, long b) {
  return Math.min(a, b);
}

static int abs(int a) {
  return Math.abs(a);
}

static long abs(long a) {
  return Math.abs(a);
}

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

static void swap(int arr[], int i, int j) {
  int temp = arr[i];
  arr[i] = arr[j];
  arr[j] = temp;
}

static int maxArr(int arr[]) {
  int maxi = Integer.MIN_VALUE;
  for (int x : arr)
    maxi = max(maxi, x);
  return maxi;
}

static int minArr(int arr[]) {
  int mini = Integer.MAX_VALUE;
  for (int x : arr)
    mini = min(mini, x);
  return mini;
}

static long maxArr(long arr[]) {
  long maxi = Long.MIN_VALUE;
  for (long x : arr)
    maxi = max(maxi, x);
  return maxi;
}

static long minArr(long arr[]) {
  long mini = Long.MAX_VALUE;
  for (long x : arr)
    mini = min(mini, x);
  return mini;
}
static int lcm(int a,int b){
  return (int)(((long)a*b)/(long)gcd(a,b));
}
static int gcd(int a, int b) {
  if (b == 0)
    return a;
  return gcd(b, a % b);
}

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

static void ruffleSort(int[] a) {
  int n = a.length;
  Random r = new Random();
  for (int i = 0; i < a.length; i++) {
    int oi = r.nextInt(n);
    int temp = a[i];
    a[i] = a[oi];
    a[oi] = temp;
  }
  Arrays.sort(a);
}

public static int binarySearch(int a[], int target) {
  int left = 0;
  int right = a.length - 1;
  int mid = (left + right) / 2;
  int i = 0;
  while (left <= right) {
    if (a[mid] <= target) {
      i = mid + 1;
      left = mid + 1;
    } else {
      right = mid - 1;
    }
    mid = (left + right) / 2;
  }
  return i-1;
}

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[] readLongArray(int n) {
    long[] a = new long[n];
    for (int i = 0; i < n; i++)
      a[i] = nextLong();
    return a;
  }

  int[][] read2dArray(int n, int m) {
    int arr[][] = new int[n][m];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        arr[i][j] = nextInt();
      }
    }
    return arr;
  }

  ArrayList<Integer> readArrayList(int n) {
    ArrayList<Integer> arr = new ArrayList<Integer>();
    for (int i = 0; i < n; i++) {
      int a = nextInt();
      arr.add(a);
    }
    return arr;
  }

  long nextLong() {
    return Long.parseLong(next());
  }
}
 static class Pair {
  int l, r;

  Pair(int fr, int sc) {
    this.l = fr;
    this.r = sc;
  }
}

////////////////////////////////////////////////////////////////////////////////////  

}