Problem: Recently, Pari and Arya did some research about NP-Hard problems and they found the minimum vertex cover problem very interesting.

Suppose the graph G is given. Subset A of its vertices is called a vertex cover of this graph, if for each edge uv there is at least one endpoint of it in this set, i.e. <image> or <image> (or both).

Pari and Arya have won a great undirected graph as an award in a team contest. Now they have to split it in two parts, but both of them want their parts of the graph to be a vertex cover.

They have agreed to give you their graph and you need to find two disjoint subsets of its vertices A and B, such that both A and B are vertex cover or claim it's impossible. Each vertex should be given to no more than one of the friends (or you can even keep it for yourself).

Input

The first line of the input contains two integers n and m (2 ≤ n ≤ 100 000, 1 ≤ m ≤ 100 000) — the number of vertices and the number of edges in the prize graph, respectively.

Each of the next m lines contains a pair of integers ui and vi (1 ≤ ui, vi ≤ n), denoting an undirected edge between ui and vi. It's guaranteed the graph won't contain any self-loops or multiple edges.

Output

If it's impossible to split the graph between Pari and Arya as they expect, print "-1" (without quotes).

If there are two disjoint sets of vertices, such that both sets are vertex cover, print their descriptions. Each description must contain two lines. The first line contains a single integer k denoting the number of vertices in that vertex cover, and the second line contains k integers — the indices of vertices. Note that because of m ≥ 1, vertex cover cannot be empty.

Examples

Input

4 2
1 2
2 3


Output

1
2 
2
1 3 


Input

3 3
1 2
2 3
1 3


Output

-1

Note

In the first sample, you can give the vertex number 2 to Arya and vertices numbered 1 and 3 to Pari and keep vertex number 4 for yourself (or give it someone, if you wish).

In the second sample, there is no way to satisfy both Pari and Arya.

Solution (in JAVA):

Solution:
///package CodeForce;

import java.io.*;
import java.util.*;
import java.text.*;
import java.math.*;
import java.util.regex.*;

public class R360C {


	static int[] A;
    static int[] S;
    static long[] sum;
   public static int mod=1000000007;
   static int[][] dp;
   static boolean[][] isPalin;
   static int max1=5000+10;
   static int[][] g;
  public static void main(String[] args) throws Exception
   {
   	InputReader in = new InputReader(System.in);
   	PrintWriter out=new PrintWriter(System.out);
   	  int n=in.ii();
   	  int m=in.ii();
   	  int[] from=new int[m];
   	  int[] to=new int[m];
   	  for(int i=0;i<m;i++)
   	  {
   		  from[i]=in.ii()-1;
   		  to[i]=in.ii()-1;
   	  }
   	int[][] graph=packU(n,from,to,m);
   	   int[] col=new int[n];
   	   Arrays.fill(col,-1);
   	   int ans=0;
   	   boolean j=true;
   	  outer: for(int i=0;i<n;i++)
   	   {
   		   if(col[i]==-1)
   		   {
   			   Queue<Integer> q=new LinkedList<Integer>();
   			   col[i]=0;
   			   q.add(i);
   			   while(!q.isEmpty())
   			   {
   				   int u=q.poll();
   				   for(int ver:graph[u])
   				   {
   					   if(col[ver]==(col[u]^1)){}
   					   else if(col[ver]==-1)
   					   {
   						   col[ver]=col[u]^1;
   						   q.add(ver);
   					   }
   					   else {
   						   ans=-1;
   						   j=false;
   						   break outer;
   					   }
   				   }
   			   }
   		   }
   	   }
   	   if(j){
      LinkedList<Integer>l1=new LinkedList<Integer>();
      LinkedList<Integer>l2=new LinkedList<Integer>();
      for(int i=0;i<n;i++)
      {
    	  if(col[i]==0)
    		  l1.add(i+1);
    	  else l2.add(i+1);
      }
   	out.println(l1.size());
   	for(int o:l1)out.print(o+" ");
   	out.println("");
   	out.println(l2.size());
   	for(int o:l2)out.print(o+" ");
   	   }
   	   else out.println(ans);
   	out.close();
   }
  public static int[][] packU(int n, int[] from, int[] to, int max) {
	    
	    int[][] g = new int[n][];
	    int[] p = new int[n];
	    for (int i = 0; i < max; i++) p[from[i]]++;
	    for (int i = 0; i < max; i++) p[to[i]]++;
	    for (int i = 0; i < n; i++) g[i] = new int[p[i]];
	    for (int i = 0; i < max; i++) {
	        g[from[i]][--p[from[i]]] = to[i];
	        g[to[i]][--p[to[i]]] = from[i];
	    }
	    return g;
	}
	public static int[][] parents3(int[][] g, int root) {
	    int n = g.length;
	    int[] par = new int[n];
	    Arrays.fill(par, -1);

	    int[] depth = new int[n];
	    depth[0] = 0;

	    int[] q = new int[n];
	    q[0] = root;
	    for (int p = 0, r = 1; p < r; p++) {
	        int cur = q[p];
	        for (int nex : g[cur]) {
	            if (par[cur] != nex) {
	                q[r++] = nex;
	                par[nex] = cur;
	                depth[nex] = depth[cur] + 1;
	            }
	        }
	    }
	    return new int[][]{par, q, depth};
	}
	public static int lower_bound(int[] nums, int target) {
        int low = 0, high = nums.length - 1;
        while (low < high) {
            int mid = low + (high - low) / 2;
            if (nums[mid] < target)
                low = mid + 1;
            else
                high = mid;
        }
        return nums[low] == target ? low : -1;
    }

    public static int upper_bound(int[] nums, int target) {
        int low = 0, high = nums.length - 1;
        while (low < high) {
            int mid = low + (high + 1 - low) / 2;
            if (nums[mid] > target)
                high = mid - 1;
            else
                low = mid;
        }
        return nums[low] == target ? low : -1;
    }
  public static boolean palin(String s)
	{
	   int i=0;
	   int j=s.length()-1;
	   while(i<j)
	   {
		   if(s.charAt(i)==s.charAt(j))
		   {
			   i++;
			   j--;
		   }
		   else return false;     
	   }
	   return true;
	}
	
    static boolean CountPs(String s,int n)
       {
    	boolean b=false;
    	     char[] S=s.toCharArray();
	       int[][] dp=new int[n][n];
	       boolean[][] p=new boolean[n][n];
	       for(int i=0;i<n;i++)p[i][i]=true;
	     
	       for(int i=0;i<n-1;i++)
	       {
	    	   if(S[i]==S[i+1])
	    	   {
	    		p[i][i+1]=true;
	    		dp[i][i+1]=1;
	    		b=true;
	    	   }
	       }
	    
	       for(int gap=2;gap<n;gap++)
	       {
	    	   for(int i=0;i<n-gap;i++)
	    	   {
	    		   int j=gap+i;
	    		   if(S[i]==S[j]&&p[i+1][j-1]){p[i][j]=true;}
	    		  
	    		  if(p[i][j])
	    			   dp[i][j]=dp[i][j-1]+dp[i+1][j]+1-dp[i+1][j-1];
	    		   
	    		   else  dp[i][j]=dp[i][j-1]+dp[i+1][j]-dp[i+1][j-1];
	    		  
	    		   if(dp[i][j]>=1){b=true;}
	    	   }
	       }
	      
	    return b; 
   // return dp[0][n-1];
	       
    }
  
  
  
 
static BigInteger power2(BigInteger x, BigInteger y, BigInteger m){
				BigInteger ans = new BigInteger("1");
				BigInteger one  = new BigInteger("1");
				BigInteger two  = new BigInteger("2");
				BigInteger zero  = new BigInteger("0");
				while(y.compareTo(zero)>0){
					//System.out.println(y);
					if(y.mod(two).equals(one)){
						ans = ans.multiply(x).mod(m);
						y = y.subtract(one);
					}
					else{
						x = x.multiply(x).mod(m);
						y = y.divide(two);
					}
				}
				return ans;
			}
			static BigInteger power(BigInteger x, BigInteger y, BigInteger m)
			{
			    if (y.equals(new BigInteger("0")))
			        return (new BigInteger("1"));
			    BigInteger p = power(x, y.divide(new BigInteger("2")), m).mod(m);
			    p = (p.multiply(p)).mod(m);

			    return (y.mod(new BigInteger("2")).equals(new BigInteger("0")))? p : (p.multiply(x)).mod(m);
		}


public static int gcd(int x,int y)
{
	if(x%y==0)
		return y;
	else
		return gcd(y,x%y);
}


public static long pow(long n,long p,long m)
{
	 long  result = 1;
	  if(p==0)
	    return 1;
	if (p==1)
	    return n;
	while(p!=0)
	{
	    if(p%2==1)
	        result *= n;
	    if(result>=m)
	    result%=m;
	    p >>=1;
	    n*=n;
	    if(n>=m)
	    n%=m;
	}
	return result;
}
public static long pow(long n,long p)
{
	long  result = 1;
	  if(p==0)
	    return 1;
	if (p==1)
	    return n;
	while(p!=0)
	{
	    if(p%2==1)
	        result *= n;
	    p >>=1;
	    n*=n;
	}
	return result;

}




static class Edge implements Comparator<Edge> {
	private int u;
	private int v;
	private int w;
	public Edge() {
	}
	public Edge(int u, int v, int w) {
		this.u=u;
		this.v=v;
		this.w=w;
	}
	public int getU() {
		return u;
	}
	public void setU(int u) {
		this.u = u;
	}
	public int getV() {
		return v;
	}
	public void setV(int v) {
		this.v = v;
	}
	public int getW() {
		return w;
	}
	public void setW(int w) {
		this.w = w;
	      }
	public int compare(Edge o1, Edge o2)
	  {
		return o2.getW() - o1.getW();
	}
	@Override
	public String toString() {
		return "Edge [u=" + u + ", v=" + v + ", w=" + w + "]";
	}
}



static class Pair implements Comparable<Pair>
{
	int a,b;
	Pair (int a,int b)
	{
		this.a=a;
		this.b=b;
	}

	public int compareTo(Pair o) {
		// TODO Auto-generated method stub
		if(this.a!=o.a)
		return -Integer.compare(this.a,o.a);
		else
			return -Integer.compare(this.b, o.b);
		//return 0;
	}
	public boolean equals(Object o) {
       if (o instanceof Pair) {
           Pair p = (Pair)o;
           return p.a == a && p.b == b;
       }
       return false;
   }
   public int hashCode() {
       return new Integer(a).hashCode() * 31 + new Integer(b).hashCode();
   }
}

static  class InputReader
{
   private InputStream stream;
   private byte[] buf = new byte[1024];

   private SpaceCharFilter filter;
    byte inbuffer[] = new byte[1024];
   int lenbuffer = 0, ptrbuffer = 0;
    final int M = (int) 1e9 + 7;
   int md=(int)(1e7+1);
    int[] SMP=new int[md];
   final double eps = 1e-6;
   final double pi = Math.PI;

	PrintWriter out;
   String check = "";
 InputStream   obj = check.isEmpty() ? System.in : new ByteArrayInputStream(check.getBytes());
   public InputReader(InputStream stream)
   {
       this.stream = stream;
   }

    int readByte() {
	        if (lenbuffer == -1) throw new InputMismatchException();
	        if (ptrbuffer >= lenbuffer) {
	            ptrbuffer = 0;
	            try {
	                lenbuffer = obj.read(inbuffer);
	            } catch (IOException e) {
	                throw new InputMismatchException();
	            }
	        }
	        if (lenbuffer <= 0) return -1;
	        return inbuffer[ptrbuffer++];
   }

   public  int read()
   {
       int c = read();
       while (isSpaceChar(c))
           c = read();
       int sgn = 1;
       if (c == '-')
       {
           sgn = -1;
           c = read();
       }
       int res = 0;
       do
       {
           if (c < '0' || c > '9')
               throw new InputMismatchException();
           res *= 10;
           res += c - '0';
           c = read();
       } while (!isSpaceChar(c));
       return res * sgn;
   }

   String is() {
	        int b = skip();
	        StringBuilder sb = new StringBuilder();
	        while (!(isSpaceChar(b))) // when nextLine, (isSpaceChar(b) && b!=' ')
	        {
	            sb.appendCodePoint(b);
	            b = readByte();
	        }
	        return sb.toString();
   }
   public   int ii() {
	        int num = 0, b;
	        boolean minus = false;
	        while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')) ;
	        if (b == '-') {
	            minus = true;
	            b = readByte();
	        }
	        while (true) {
	            if (b >= '0' && b <= '9') {
	                num = num * 10 + (b - '0');
	            } else {
	                return minus ? -num : num;
	            }
	            b = readByte();
	        }
   }
 public   long il() {
	        long num = 0;
	        int b;
	        boolean minus = false;
	        while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')) ;
	        if (b == '-') {
	            minus = true;
	            b = readByte();
	        }
	        while (true) {
	            if (b >= '0' && b <= '9') {
	                num = num * 10 + (b - '0');
	            } else {
	                return minus ? -num : num;
	            }
	            b = readByte();
	        }
   }
    public int root(int i)
		     {
				 while(A[i]!=i)
				 {
					A[i]=A[A[i]];
					i=A[i];
				 }


				 return i;
			 }

		   public void union(int a,int b )
		   {
			   int r1=root(a);
			   int r2=root(b);
			     if(S[r1]>S[r2])
			   		{
			   			A[r2]=r1;
			   			S[r1]+=S[r2];
			   			S[r2]=0;
			   		}
			   		else
			   		{
			   			A[r1]=r2;
			   			S[r2]+=S[r1];
			   			S[r1]=0;
			        }

	      }

	    boolean isSpaceChar(int c) {
	        return (!(c >= 33 && c <= 126));
	       }

	      int skip()
	        {
	        int b;
	        while ((b = readByte()) != -1 && isSpaceChar(b)) ;
	        return b;
	        }

	    float nf() {
	        return Float.parseFloat(is());
	    }

	    double id() {
	        return Double.parseDouble(is());
	    }

	    char ic() {
	        return (char) skip();
	    }

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

	    long[] ila(int n) {
	        long a[] = new long[n+1];
	        for (int i = 1; i <=n; i++) a[i] = il();
	        return a;
	    }

	    String[] isa(int n) {
	        String a[] = new String[n];
	        for (int i = 0; i < n; i++) a[i] = is();
	        return a;
	    }


		 long mul(long a, long b) { return a * b % M; }

			long div(long a, long b)
				 {
					return mul(a, pow(b, M - 2));

		           }



	    double[][] idm(int n, int m) {
	        double a[][] = new double[n][m];
	        for (int i = 0; i < n; i++) for (int j = 0; j < m; j++) a[i][j] = id();
	        return a;
	        }

	    int[][] iim(int n, int m) {
	        int a[][] = new int[n][m];
	        for (int i = 0; i < n; i++) for (int j = 0; j <m; j++) a[i][j] = ii();
	        return a;
          }


   public String readLine() {
       int c = read();
       while (isSpaceChar(c))
           c = read();
       StringBuilder res = new StringBuilder();
       do {
           res.appendCodePoint(c);
           c = read();
       } while (!isEndOfLine(c));
       return res.toString();
   }

   public interface SpaceCharFilter
   {
       public boolean isSpaceChar(int ch);
   }
   public boolean isEndOfLine(int c) {
       return c == '\n' || c == '\r' || c == -1;
   }
}

}