A tree is a connected undirected graph consisting of n vertices and n - 1 edges. Vertices are numbered 1 through n.

Limak is a little polar bear and Radewoosh is his evil enemy. Limak once had a tree but Radewoosh stolen it. Bear is very sad now because he doesn't remember much about the tree — he can tell you only three values n, d and h:

  * The tree had exactly n vertices. 
  * The tree had diameter d. In other words, d was the biggest distance between two vertices. 
  * Limak also remembers that he once rooted the tree in vertex 1 and after that its height was h. In other words, h was the biggest distance between vertex 1 and some other vertex. 



The distance between two vertices of the tree is the number of edges on the simple path between them.

Help Limak to restore his tree. Check whether there exists a tree satisfying the given conditions. Find any such tree and print its edges in any order. It's also possible that Limak made a mistake and there is no suitable tree – in this case print "-1".

Input

The first line contains three integers n, d and h (2 ≤ n ≤ 100 000, 1 ≤ h ≤ d ≤ n - 1) — the number of vertices, diameter, and height after rooting in vertex 1, respectively.

Output

If there is no tree matching what Limak remembers, print the only line with "-1" (without the quotes).

Otherwise, describe any tree matching Limak's description. Print n - 1 lines, each with two space-separated integers – indices of vertices connected by an edge. If there are many valid trees, print any of them. You can print edges in any order.

Examples

Input

5 3 2


Output

1 2
1 3
3 4
3 5

Input

8 5 2


Output

-1


Input

8 4 2


Output

4 8
5 7
2 3
8 1
2 1
5 6
1 5

Note

Below you can see trees printed to the output in the first sample and the third sample.

<image>
import java.util.*;
import java.io.*;
	import java.lang.*;
	
	public class graph1
	{
		public static int n;
		public static ArrayList<Integer> adj[];
		public static ArrayList<Integer> adjrev[];
		
		public static ArrayList<Integer> child[];
		public static boolean[] vis;
		public static int[] par;
		public static int[] level;
		public static int[] set;
		public static int count = 1;
		public static int count2 = 1;
		
		public static long[] arr;
		public static triplet[] trp;;
		public static HashSet<Integer> hset[];
		public static ArrayList<Integer> path[];
		
		
		
		
		public static void bfs(int x)
		{
			Queue<Integer> queue = new LinkedList<>();
			queue.add(x);
			//level[x] = 1;
			
			//parent[x] = 0;
			vis[x] = true;
			if(set[x]==0)
				set[x] = count;
			while(!queue.isEmpty())
			{
				int last = queue.poll();
				for(int p : adj[last])
				{
					if(!vis[p])
					{
							//	children[last].add(a);
						queue.add(p);
					//	System.out.println(p+" ");
						
						vis[p] = true;
						set[p] = count;
					//	parent[a] = last;
						//level[a] = level[last]+1;
						
					}
				}
			}
		}
		
		
		

		public static boolean dfs(int s)
		{
			Stack<Integer> stk = new Stack<>();
	 		stk.add(s);
			par[s] = 0;
			vis[s] = true;
			level[s] = 1;
			boolean flag = true;
			while(!stk.isEmpty())
			{
				int last = stk.pop();
			///	System.out.println(last);
				boolean f = false;
				for(int a : adj[last])
				{
					if(!vis[a])
					{
						//child[last].add(a);
						stk.add(a);
						par[a] = last;
						level[a] = level[last] +1;
						vis[a] = true;
					}
				}
			
			}
			return flag;
		}
				
	
		
		public static void dfsrec(int s)
		{
			if(vis[s])
				return;
			
			vis[s] = true;
			int k = 0;
			for(int p: adj[s])
			{
				count2 = count;
				boolean f2 = false;
				if(!hset[count].contains(s))
					f2 = true;
				if(!vis[p])
				{
					k++;
					if(f2)
						path[count].add(s);
					path[count].add(p);
					dfsrec(p);
				}
				
			}
			par[s] = k;
			count++;
			
		}
		
		public static int find(int i) {
			
			
			if(par[i]==-1)
				return i;
			else
				return find(par[i]);
				
		}
		
		 public static void union( int x, int y)
		    {
		        int xset = find( x);
		        int yset = find(y);
		        par[xset] = yset;
		    }

		
		
		 public static boolean cycle(HashSet<pair> set) {
			 
			 
			 for(pair p: set)
			 {
				 int x = find(p.x);
				 int y = find(p.y);
				 if(x==y)
					 return true;
		
				 union(x, y);
				 
			 }
			 
			 return false;
		 }
		
		
		
		
		
		
		
		public static void main(String[] args)
		{
			InputReader in = new InputReader(System.in);
			PrintWriter pw = new PrintWriter(System.out);
	
	//		n = in.nextInt();
			int n = in.nextInt();
			
			/*adj = new ArrayList[n+1];
			
			
			//children = new ArrayList[n+1];
			vis = new boolean[n+1];
			/*for(int i=0; i<=n; i++)
			{
				//vis [i] = false;
				par[i] = -1;
			}
			
			
			
			path = new ArrayList[n+1];
			hset = new HashSet[n+1];
			par = new int[n+1];
			for(int i=0;i<=n;i++)
			{
				adj[i] = new ArrayList<Integer>();
				path[i] = new ArrayList<>();
				hset[i] = new HashSet<>();
			}
	
			for(int i=0; i<n-1; i++)
			{
				int v = in.nextInt();
				int u = in.nextInt();
				adj[v].add(u);
				adj[u].add(v);
				
			}
			*/
			
			
			int d = in.nextInt();
			int h = in.nextInt();
			
			
			if(2*h<d || (d)>=n  || h>=n || h>d)
				pw.print(-1);
			else if(h==d )
			{
				if(h>=2 || (h==1 && n==2))
				{
				int count = 2;
				for(int i=0; i<h; i++)
				{
					pw.println(count-1+" "+count);
					count++;
				}
				for(int i=count; i<=n; i++)
				{
					pw.println(2+" "+i);
				}
				}
				else
					pw.print(-1);
			}
			
			else
			{
				
				{
				int count = 2;
				for(int i=0; i<h; i++) {
					
					pw.println(count-1+" "+(count));
					count++;
				}
				
				int k = d - h;
				pw.println(1+" "+count);
				count++;
				for(int i=0; i<k-1; i++)
				{
					pw.println(count-1+" "+(count));
					count++;
				}
				for(int i=count; i<=n; i++)
					pw.println(1+" "+(i));
				
				
				}
			
			}
			
			
			//code ends....
			pw.flush();
			pw.close();
		}
		
		static class pair implements Comparable<pair>
		 
		{
			Integer x, y;
			pair(int x,int y)
			{
		
				this.x=x;
				this.y=y;
			}
			
			public int compareTo(pair o) {
				int result = x.compareTo(o.x);
				if(result==0)
					result = y.compareTo(o.y);
				
				return result;
			}  
			
			public String toString()
			{
				return x+" "+y;
			}
			
			public boolean equals(Object o)
			{
				if (o instanceof pair)
			    {
					pair p = (pair)o;
					return p.x == x && p.y == y ;
				}
				return false;
			}
			
			public int hashCode()
			{
				return new Long(x).hashCode()*31 + new Long(y).hashCode();
			}
		}
	
	
		static class triplet implements Comparable<triplet>
		{
			Integer x,y,z;
			triplet(int x,int y,int z)
			{
				this.x = x;
				this.y = y;
				this.z = z;
			}
			
			public  int compareTo(triplet o)
			{
				int result = x.compareTo(o.x);
				if(result==0)
					result =  y.compareTo(o.y);
				if(result==0)
					result = z.compareTo(o.z);
	
				return result;
			}
			
			public boolean equlas(Object o)
			{
				if(o instanceof triplet)
				{
					triplet p = (triplet)o;
					return x==p.x && y==p.y && z==p.z;
				}
				return false;
			}
			
			public String toString()
			{
				return x+" "+y+" "+z;
			}
			public int hashCode()
			{
				return new Long(x).hashCode()*31 + new Long(y).hashCode() + new Long(z).hashCode(); 
			}
		}
		
	
		
		
		
		static class InputReader 
		{
			 
			private final InputStream stream;
			private final byte[] buf = new byte[8192];
			private int curChar, snumChars;
			private SpaceCharFilter filter;
	 
			public InputReader(InputStream stream) 
			{
				this.stream = stream;
			}
	 
			public int snext() 
			{
				if (snumChars == -1)
					throw new InputMismatchException();
				if (curChar >= snumChars) 
				{
					curChar = 0;
					try 
					{
						snumChars = stream.read(buf);
					} 
					catch (IOException e) 
					{
						throw new InputMismatchException();
					}
					if (snumChars <= 0)
						return -1;
				}
				return buf[curChar++];
			}
	 
			public int nextInt() 
		    {
				int c = snext();
				while (isSpaceChar(c)) 
				{
					c = snext();
				}
				int sgn = 1;
				if (c == '-')
			    {
					sgn = -1;
					c = snext();
				}
				int res = 0;
				do 
				{
					if (c < '0' || c > '9')
						throw new InputMismatchException();
					res *= 10;
					res += c - '0';
					c = snext();
				} while (!isSpaceChar(c));
				return res * sgn;
			}
	 
			public long nextLong()
		    {
				int c = snext();
				while (isSpaceChar(c)) 
				{
					c = snext();
				}
				int sgn = 1;
				if (c == '-') 
				{
					sgn = -1;
					c = snext();
				}
				long res = 0;
				do 
				{
					if (c < '0' || c > '9')
						throw new InputMismatchException();
					res *= 10;
					res += c - '0';
					c = snext();
				} while (!isSpaceChar(c));
				return res * sgn;
			}
	 
			public int[] nextIntArray(int n) 
			{
				int a[] = new int[n];
				for (int i = 0; i < n; i++) 
				{
					a[i] = nextInt();
				}
				return a;
			}
	 
			public String readString()
		    {
				int c = snext();
				while (isSpaceChar(c)) 
				{
					c = snext();
				}
				StringBuilder res = new StringBuilder();
				do 
				{
					res.appendCodePoint(c);
					c = snext();
				} while (!isSpaceChar(c));
				return res.toString();
			}
	 
			public String nextLine() 
			{
				int c = snext();
				while (isSpaceChar(c))
					c = snext();
				StringBuilder res = new StringBuilder();
				do 
				{
					res.appendCodePoint(c);
					c = snext();
				} while (!isEndOfLine(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;
			}
	 
			private boolean isEndOfLine(int c) 
			{
				return c == '\n' || c == '\r' || c == -1;
			}
	 
			public interface SpaceCharFilter
		    {
				public boolean isSpaceChar(int ch);
			}
		}
		
		public static long mod = 1000000007;
		public static int d;
		public static int p;
		public static int q;
		
		public static int[] suffle(int[] a,Random gen)
		{
			int n = a.length;
			for(int i=0;i<n;i++)
			{
				int ind = gen.nextInt(n-i)+i;
				int temp = a[ind];
				a[ind] = a[i];
				a[i] = temp;
			}
			return a;
		}
		
		public static void swap(int a, int b){
			int temp = a;
			a = b;
			b = temp;
		}
		
		public static HashSet<Integer> primeFactorization(int n)
		{
			HashSet<Integer> a =new HashSet<Integer>();
			for(int i=2;i*i<=n;i++)
			{
				while(n%i==0)
				{
					a.add(i);
					n/=i;
				}
			}
			if(n!=1)
				a.add(n);
			return a;
		}
		
		public static void sieve(boolean[] isPrime,int n)
		{
			for(int i=1;i<n;i++)
				isPrime[i] = true;
			
			isPrime[0] = false;
			isPrime[1] = false;
			
			for(int i=2;i*i<n;i++)
			{
				if(isPrime[i] == true)
				{
					for(int j=(2*i);j<n;j+=i)
						isPrime[j] = false;
				}
			}
		}
		
		public static int GCD(int a,int b)
		{
			if(b==0)
				return a;
			else
				return GCD(b,a%b);
		}
		
		public static long GCD(long a,long b)
		{
			if(b==0)
				return a;
			else
				return GCD(b,a%b);
		}
		
		public static void extendedEuclid(int A,int B)
		{
			if(B==0)
			{
				d = A;
				p = 1 ;
				q = 0;
			}
			else
			{
				extendedEuclid(B, A%B);
				int temp = p;
				p = q;
				q = temp - (A/B)*q;
			}
		}
		
		public static long LCM(long a,long b)
		{
			return (a*b)/GCD(a,b);
		}
		
		public static int LCM(int a,int b)
		{
			return (a*b)/GCD(a,b);
		}
		
		public static int binaryExponentiation(int x,int n)
		{
		    int result=1;
		    while(n>0)
		    {
		        if(n % 2 ==1)
		            result=result * x;
		        x=x*x;
		        n=n/2;
		    }
		    return result;
		}
		
		public static long binaryExponentiation(long x,long n)
		{
		    long result=1;
		    while(n>0)
		    {
		        if(n % 2 ==1)
		            result=result * x;
		        x=x*x;
		        n=n/2;
		    }
		    return result;
		}
		
		public static int modularExponentiation(int x,int n,int M)
		{
		    int result=1;
		    while(n>0)
		    {
		        if(n % 2 ==1)
		            result=(result * x)%M;
		        x=(x*x)%M;
		        n=n/2;
		    }
		    return result;
		}
		
		public static long modularExponentiation(long x,long n,long M)
		{
		    long result=1;
		    while(n>0)
		    {
		        if(n % 2 ==1)
		            result=(result * x)%M;
		        x=(x*x)%M;
		        n=n/2;
		    }
		    return result;
		}
		
		public static int modInverse(int A,int M)
		{
		    return modularExponentiation(A,M-2,M);
		}
		
		public static long modInverse(long A,long M)
		{
		    return modularExponentiation(A,M-2,M);
		}
		
		
		
		
		
		public static boolean isPrime(int n)
		{
		    
		    if (n <= 1)  return false;
		    if (n <= 3)  return true;
		    
		    if (n%2 == 0 || n%3 == 0) 
		    	return false;
		 
		    for (int i=5; i*i<=n; i=i+6)
		    {
		        if (n%i == 0 || n%(i+2) == 0)
		           return false;
		    }
		    
		    return true;
		}
		
		
	}