You are given three integers n, d and k.

Your task is to construct an undirected tree on n vertices with diameter d and degree of each vertex at most k, or say that it is impossible.

An undirected tree is a connected undirected graph with n - 1 edges.

Diameter of a tree is the maximum length of a simple path (a path in which each vertex appears at most once) between all pairs of vertices of this tree.

Degree of a vertex is the number of edges incident to this vertex (i.e. for a vertex u it is the number of edges (u, v) that belong to the tree, where v is any other vertex of a tree).

Input

The first line of the input contains three integers n, d and k (1 ≤ n, d, k ≤ 4 ⋅ 10^5).

Output

If there is no tree satisfying the conditions above, print only one word "NO" (without quotes).

Otherwise in the first line print "YES" (without quotes), and then print n - 1 lines describing edges of a tree satisfying the conditions above. Vertices of the tree must be numbered from 1 to n. You can print edges and vertices connected by an edge in any order. If there are multiple answers, print any of them.1

Examples

Input

6 3 3


Output

YES
3 1
4 1
1 2
5 2
2 6


Input

6 2 3


Output

NO


Input

10 4 3


Output

YES
2 9
2 10
10 3
3 1
6 10
8 2
4 3
5 6
6 7


Input

8 5 3


Output

YES
2 5
7 2
3 7
3 1
1 6
8 7
4 3
import java.util.*;
import java.io.*; 
import java.text.DecimalFormat;

public class Main{
    final long mod = (int)1e9+7, IINF = (long)1e19;
    final int MAX = (int)1e6+1, MX = (int)1e7+1, INF = (int)1e9, root = 3;
    DecimalFormat df = new DecimalFormat("0.0000000000000");
    double eps = 1e-9, pi = 3.141592653589793238462643383279502884197169399375105820974944;
    static boolean multipleTC = false, memory = false;
    FastReader in;PrintWriter out;
    public static void main(String[] args) throws Exception{
        if(memory)new Thread(null, new Runnable() {public void run(){try{new Main().run();}catch(Exception e){e.printStackTrace();}}}, "1", 1 << 28).start();
        else new Main().run();
    }

    void run() throws Exception{
        in = new FastReader();
        out = new PrintWriter(System.out);
        for(int i = 1, T= (multipleTC)?ni():1; i<= T; i++)solve(i);
        out.flush();
        out.close();
    }
    
    void solve(int TC) throws Exception{
        int n = ni(), d = ni(), k = ni();
        boolean imp = false;
        if(n==1){
            pn("NO");return;
        }
        else if(n==2){
            if(d==1){
                pn("YES");
                pn("1 2");
            }else pn("NO");
            return;
        }
        else if(k==1 || d>=n){
            pn("NO");return;
        }
        int[][] edge = new int[n-1][2];
        int c = 0;int[] deg = new int[n];
        for(int i = 0; i< d && !imp; i++){
            deg[i]++;deg[i+1]++;
            edge[c++] = new int[]{1+i,i+2};
        }
        int[] di = new int[n];
        TreeSet<Integer> set = new TreeSet<>();
        for(int i = 0; i<= d && !imp; i++){
            di[i] = Math.min(i-0, d-i);
            if(di[i]>0 && deg[i]<k){
                set.add(i);
            }
        }
        for(int i = d+1; i< n && !imp; i++){
            if(set.isEmpty())imp = true;
            else{
                int x = set.first();
                deg[x]++;
                di[i] = di[x]-1;
                deg[i] = 1;
                edge[c++] = new int[]{x+1,i+1};
                if(deg[x]==k)set.remove(x);
                if(di[i]>0)set.add(i);
            }
        }
        if(imp){pn("NO");return;}
            pn("YES");
        for(int i = 0; i< c; i++)pn(edge[i][0]+" " + edge[i][1]);
        
    }
    
    int[] reverse(int[] a){
        int[] o = new int[a.length];
        for(int i = 0; i< a.length; i++)o[i] = a[a.length-i-1];
        return o;   
    }

    int[] sort(int[] a){
        if(a.length==1)return a;
        int mid = a.length/2;
        int[] b = sort(Arrays.copyOfRange(a,0,mid)), c = sort(Arrays.copyOfRange(a,mid,a.length));
        for(int i = 0, j = 0, k = 0; i< a.length; i++){
            if(j<b.length && k<c.length){
                if(b[j]<c[k])a[i] = b[j++];
                else a[i] = c[k++];
            }else if(j<b.length)a[i] = b[j++];
            else a[i] = c[k++];
        }
        return a;
    }

    long[] sort(long[] a){
        if(a.length==1)return a;
        int mid = a.length/2;
        long[] b = sort(Arrays.copyOfRange(a,0,mid)), c = sort(Arrays.copyOfRange(a,mid,a.length));
        for(int i = 0, j = 0, k = 0; i< a.length; i++){
            if(j<b.length && k<c.length){
                if(b[j]<c[k])a[i] = b[j++];
                else a[i] = c[k++];
            }else if(j<b.length)a[i] = b[j++];
            else a[i] = c[k++];
        }
        return a;
    }

    long gcd(long a, long b){return (b==0)?a:gcd(b,a%b);}
    int gcd(int a, int b){return (b==0)?a:gcd(b,a%b);}
    int bitcount(long n){return (n==0)?0:(1+bitcount(n&(n-1)));}
    void p(Object o){out.print(o);}
    void pn(Object o){out.println(o);}
    void pni(Object o){out.println(o);out.flush();}
    String n(){return in.next();}
    String nln(){return in.nextLine();}
    int ni(){return Integer.parseInt(in.next());}
    long nl(){return Long.parseLong(in.next());}
    double nd(){return Double.parseDouble(in.next());}

    class FastReader{
        BufferedReader br;
        StringTokenizer st;
        public FastReader(){
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        public FastReader(String s) throws Exception{
            br = new BufferedReader(new FileReader(s));
        }

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

        String nextLine(){
            String str = "";
            try{
                str = br.readLine();
            }catch (IOException e){
                e.printStackTrace();
            }   
            return str;
        }
    }
} 