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.*;
import java.util.*;

/**
 __                  __
 ( _)                ( _)
 / / \\              / /\_\_
 / /   \\            / / | \ \
 / /     \\          / /  |\ \ \
 /  /   ,  \ ,       / /   /|  \ \
 /  /    |\_ /|      / /   / \   \_\
 /  /  |\/ _ '_| \   / /   /   \    \\
 |  /   |/  0 \0\    / |    |    \    \\
 |    |\|      \_\_ /  /    |     \    \\
 |  | |/    \.\ o\o)  /      \     |    \\
 \    |     /\\`v-v  /        |    |     \\
 | \/    /_| \\_|  /         |    | \    \\
 | |    /__/_ `-` /   _____  |    |  \    \\
 \|    [__]  \_/  |_________  \   |   \    ()
 /    [___] (    \         \  |\ |   |   //
 |    [___]                  |\| \|   /  |/
 /|    [____]                  \  |/\ / / ||
 (  \   [____ /     ) _\      \  \    \| | ||
 \  \  [_____|    / /     __/    \   / / //
 |   \ [_____/   / /        \    |   \/ //
 |   /  '----|   /=\____   _/    |   / //
 __ /  /        |  /   ___/  _/\    \  | ||
 (/-(/-\)       /   \  (/\/\)/  |    /  | /
 (/\/\)           /   /   //
 _________/   /    /
 \____________/    (


 @author NTUDragons-Reborn
 */

public class C{
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        Task solver = new Task();
        solver.solve(in, out);
        out.close();
    }
    // main solver
    static class Task{

        double eps= 0.00000001;
        static final int MAXN = 200015;
        static final int MOD= 1000000007;

        // stores smallest prime factor for every number
        static int spf[] = new int[MAXN];

        static boolean[] prime;

        Map<Integer,Set<Integer>> dp= new HashMap<>();

        // Calculating SPF (Smallest Prime Factor) for every
        // number till MAXN.
        // Time Complexity : O(nloglogn)
        public void sieve()
        {
            spf[1] = 1;
            for (int i=2; i<MAXN; i++)

                // marking smallest prime factor for every
                // number to be itself.
                spf[i] = i;

            // separately marking spf for every even
            // number as 2
            for (int i=4; i<MAXN; i+=2)
                spf[i] = 2;

            for (int i=3; i*i<MAXN; i++)
            {
                // checking if i is prime
                if (spf[i] == i)
                {
                    // marking SPF for all numbers divisible by i
                    for (int j=i*i; j<MAXN; j+=i)

                        // marking spf[j] if it is not
                        // previously marked
                        if (spf[j]==j)
                            spf[j] = i;
                }
            }
        }

        void sieveOfEratosthenes(int n)
        {
            // Create a boolean array
            // "prime[0..n]" and
            // initialize all entries
            // it as true. A value in
            // prime[i] will finally be
            // false if i is Not a
            // prime, else true.
            prime= new boolean[n + 1];
            for (int i = 0; i <= n; i++)
                prime[i] = true;
    
            for (int p = 2; p * p <= n; p++)
            {
                // If prime[p] is not changed, then it is a
                // prime
                if (prime[p] == true)
                {
                    // Update all multiples of p
                    for (int i = p * p; i <= n; i += p)
                        prime[i] = false;
                }
            }
        }

        // A O(log n) function returning primefactorization
        // by dividing by smallest prime factor at every step
        public Set<Integer> getFactorization(int x)
        {
            if(dp.containsKey(x)) return dp.get(x);
            Set<Integer> ret = new HashSet<>();
            while (x != 1)
            {
                if(spf[x]!=2) ret.add(spf[x]);
                x = x / spf[x];
            }
            dp.put(x,ret);
            return ret;
        }
        // function to find first index >= x
        public int lowerIndex(List<Integer> arr, int n, int x)
        {
            int l = 0, h = n - 1;
            while (l <= h)
            {
                int mid = (l + h) / 2;
                if (arr.get(mid) >= x)
                    h = mid - 1;
                else
                    l = mid + 1;
            }
            return l;
        }
        public int lowerIndex(int[] arr, int n, int x)
        {
            int l = 0, h = n - 1;
            while (l <= h)
            {
                int mid = (l + h) / 2;
                if (arr[mid] >= x)
                    h = mid - 1;
                else
                    l = mid + 1;
            }
            return l;
        }

        // function to find last index <= y
        public int upperIndex(List<Integer> arr, int n, int y)
        {
            int l = 0, h = n - 1;
            while (l <= h)
            {
                int mid = (l + h) / 2;
                if (arr.get(mid) <= y)
                    l = mid + 1;
                else
                    h = mid - 1;
            }
            return h;
        }
        public int upperIndex(int[] arr, int n, int y)
        {
            int l = 0, h = n - 1;
            while (l <= h)
            {
                int mid = (l + h) / 2;
                if (arr[mid] <= y)
                    l = mid + 1;
                else
                    h = mid - 1;
            }
            return h;
        }

        // function to count elements within given range
        public int countInRange(List<Integer> arr, int n, int x, int y)
        {
            // initialize result
            int count = 0;
            count = upperIndex(arr, n, y) -
                    lowerIndex(arr, n, x) + 1;
            return count;
        }

        public int add(int a, int b){
            a+=b;
            if(a>=MOD) a-=MOD;
            else if(a<0) a+=MOD;
            return a;
        }

        public int mul(int a, int b){
            long res= (long)a*(long)b;
            return (int)(res%MOD);
        }

        public int power(int a, int b) {
            int ans=1;
            while(b>0){
                if((b&1)!=0) ans= mul(ans,a);
                b>>=1;
                a= mul(a,a);
            }
            return ans;
        }

        int[] fact= new int[MAXN];
        int[] inv= new int[MAXN];

        public int Ckn(int n, int k){
            if(k<0 || n<0) return 0;
            return mul(mul(fact[n],inv[k]),inv[n-k]);
        }

        public int inverse(int a){
            return power(a,MOD-2);
        }

        public void preprocess() {
            fact[0]=1;
            for(int i=1;i<MAXN;i++) fact[i]= mul(fact[i-1],i);
            inv[MAXN-1]= inverse(fact[MAXN-1]);
            for(int i=MAXN-2;i>=0;i--){
                inv[i]= mul(inv[i+1],i+1);
            }
        }

        /**
         * return VALUE of lower bound for unsorted array
         */
        public int lowerBoundNormalArray(int[] arr, int x){
            TreeSet<Integer> set= new TreeSet<>();
            for(int num: arr) set.add(num);
            return set.lower(x);
        }
        /**
         * return VALUE of upper bound for unsorted array
         */
        public int upperBoundNormalArray(int[] arr, int x){
            TreeSet<Integer> set= new TreeSet<>();
            for(int num: arr) set.add(num);
            return set.higher(x);
        }

        public void debugArr(int[] arr){
            for(int i: arr) out.print(i+" ");
            out.println();
        }

        public int rand(){
            int min=0, max= MAXN;
            int random_int = (int)Math.floor(Math.random()*(max-min+1)+min);
            return random_int;
        }
        
        InputReader in; PrintWriter out;
        CustomFileReader cin;
        int[] xor= new int[3*100000+5];
        public void solve(InputReader in, PrintWriter out) {
            this.in=in; this.out=out;
            // cin= new CustomFileReader("../HackerCup21//realA.txt");
            // preprocess();
            int t=in.nextInt();
            // int t= cin.nextIntArrLine()[0]; 
            for(int i=1;i<=t;i++) solveB(i);
        }
        public void solveA(int t){
            

        }
        public void solveB(int t) {
            long n= in.nextLong(), m= in.nextLong(), k= in.nextLong();
            if (n == 1 && m == 0 && k >= 2){
                out.println("YES"); return;
            }
            if (m > n * (n - 1)/2 ||m < n - 1 || k <= 2){
                out.println("NO"); return;
            }
            if (m ==  n * (n - 1) / 2){
                out.println("YES"); return;
            }
            else{
                out.println(k <= 3  ? "NO" : "YES"); return;
            }

        }
        public void solveC(int t){
        
        }
        public int _gcd(int a,  int b)
        {

            if(b == 0) {
                return a;
            }
            else {
                return _gcd(b, a % b);
            }
        }
        public int _lcm(int a, int b){
            return (a*b)/_gcd(a,b);
        }

    }


    static class SEG {
        public long _gcd(long a,  long  b)
        {

            if(b == 0) {
                return a;
            }
            else {
                return _gcd(b, a % b);
            }
        }
        long[] segs;
        public SEG(List<Long> a) {
            int n= a.size();
            segs= new long[4*n];
            build(0,a,0,n-1);
        }
        void build(int root, List<Long> a, int l, int r){
            if (l==r){
                segs[root] = a.get(l); return;
            }
            int m = (l+r) >> 1;
            build(root*2+1, a, l, m);
            build(root*2+2, a, m+1, r);
            segs[root] = _gcd(segs[root*2+1], segs[root*2+2]);
        }
        long query(int root, int l, int r, int lq, int rq){
            if (lq > r || rq < l) return 0l;
            if (l >= lq && rq >= r) return segs[root];
            int m = (l+r)>>1;
            return _gcd(query(root*2+1, l, m, lq, rq),
                         query(root*2+2, m+1, r, lq, rq));
        }
    }

    static class BIT {
        int MAXN= 200015;
        int BITree[] = new int[MAXN];
     
        /* n --> No. of elements present in input array.
        BITree[0..n] --> Array that represents Binary
                        Indexed Tree.
        arr[0..n-1] --> Input array for which prefix sum
                        is evaluated. */
    
        // Returns sum of arr[0..index]. This function
        // assumes that the array is preprocessed and
        // partial sums of array elements are stored
        // in BITree[].
        public int getSum(int index)
        {
            int sum = 0; // Initialize result
        
            // index in BITree[] is 1 more than
            // the index in arr[]
            index = index + 1;
        
            // Traverse ancestors of BITree[index]
            while(index>0)
            {
                // Add current element of BITree
                // to sum
                sum += BITree[index];
        
                // Move index to parent node in
                // getSum View
                index -= index & (-index);
            }
            return sum;
        }
    
        // Updates a node in Binary Index Tree (BITree)
        // at given index in BITree. The given value
        // 'val' is added to BITree[i] and all of
        // its ancestors in tree.
        public void updateBIT(int n, int index,
                                            int val)
        {
            // index in BITree[] is 1 more than
            // the index in arr[]
            index = index + 1;
        
            // Traverse all ancestors and add 'val'
            while(index <= n)
            {
            // Add 'val' to current node of BIT Tree
            BITree[index] += val;
        
            // Update index to that of parent
            // in update View
            index += index & (-index);
            }
        }
    
        /* Function to construct fenwick tree
        from given array.*/
        void constructBITree(int arr[], int n)
        {
            // Initialize BITree[] as 0
            for(int i=1; i<=n; i++)
                BITree[i] = 0;
        
            // Store the actual values in BITree[]
            // using update()
            for(int i = 0; i < n; i++)
                updateBIT(n, i, arr[i]);
        }
    }

    static class Venice{
        public Map<Long,Long> m= new HashMap<>();
        public long base=0;
        public long totalValue=0;
        private int M= 1000000007;

        private long addMod(long a, long b){
            a+=b;
            if(a>=M) a-=M;
            return a;
        }

        public void reset(){
            m= new HashMap<>();
            base=0;
            totalValue=0;
        }
        public void update(long add){
            base= base+ add;
        }
        public void add(long key, long val){
            long newKey= key-base;
            m.put(newKey, addMod(m.getOrDefault(newKey,(long)0),val));
        }
    }



    static class Tuple implements Comparable<Tuple>{
        int x, y, z;
        public Tuple(int x, int y, int z){
            this.x= x;
            this.y= y;
            this.z=z;
        }
        @Override
        public int compareTo(Tuple o){
            if(this.x!=o.x) return this.x-o.x;
            if(this.y!=o.y) return this.y-o.y;
            return this.z-o.z;
        }
    }

    static class Pair implements Comparable<Pair>{
        public int x;
        public int y;
        public Pair(int x, int y){
            this.x= x;
            this.y= y;
        }

        @Override
        public int compareTo(Pair o) {
            return this.x-o.x;
        }
    }

    // public static class compareL implements Comparator<Tuple>{
    //     @Override
    //     public int compare(Tuple t1, Tuple t2) {
    //         return t2.l - t1.l;
    //     }
    // }

    // fast input reader class;
    static class InputReader {
        BufferedReader br;
        StringTokenizer st;

        public InputReader(InputStream stream) {
            br = new BufferedReader(new InputStreamReader(stream));
        }

        public String nextToken() {
            while (st == null || !st.hasMoreTokens()) {
                String line = null;
                try {
                    line = br.readLine();
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
                if (line == null) {
                    return null;
                }
                st = new StringTokenizer(line);
            }
            return st.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(nextToken());
        }
        public double nextDouble(){
            return Double.parseDouble(nextToken());
        }
        public long nextLong(){
            return Long.parseLong(nextToken());
        }
        public int[] nextIntArr(int n){
            int[] arr= new int[n];
            for(int i=0;i<n;i++) arr[i]= nextInt();
            return arr;
        }
        public long[] nextLongArr(int n){
            long[] arr= new long[n];
            for(int i=0;i<n;i++) arr[i]= nextLong();
            return arr;
        }
        public List<Integer> nextIntList(int n){
            List<Integer> arr= new ArrayList<>();
            for(int i=0;i<n;i++) arr.add(nextInt());
            return arr;
        }
        public int[][] nextIntMatArr(int n, int m){
            int[][] mat= new int[n][m];
            for(int i=0;i<n;i++) for(int j=0;j<m;j++) mat[i][j]= nextInt();
            return mat;
        }
        public List<List<Integer>> nextIntMatList(int n, int m){
            List<List<Integer>> mat= new ArrayList<>();
            for(int i=0;i<n;i++){
                List<Integer> temp= new ArrayList<>();
                for(int j=0;j<m;j++) temp.add(nextInt());
                mat.add(temp);
            }
            return mat;
        }
        public char[] nextStringCharArr(){
            return nextToken().toCharArray();
        }
    }

    static class CustomFileReader{
        String path="";
        Scanner sc;
        public CustomFileReader(String path){
            this.path=path;
            try{
                sc= new Scanner(new File(path));
            }
            catch(Exception e){}
        }
        public String nextLine(){
            return sc.nextLine();
        }
        public int[] nextIntArrLine(){
            String line= sc.nextLine();
            String[] part= line.split("[\\s+]");
            int[] res= new int[part.length];
            for(int i=0;i<res.length;i++) res[i]= Integer.parseInt(part[i]);
            return res;
        }
    }
}