Problem: Don't you tell me what you think that I can be

If you say that Arkady is a bit old-fashioned playing checkers, you won't be right. There is also a modern computer game Arkady and his friends are keen on. We won't discuss its rules, the only feature important to this problem is that each player has to pick a distinct hero in the beginning of the game.

There are 2 teams each having n players and 2n heroes to distribute between the teams. The teams take turns picking heroes: at first, the first team chooses a hero in its team, after that the second team chooses a hero and so on. Note that after a hero is chosen it becomes unavailable to both teams.

The friends estimate the power of the i-th of the heroes as p_i. Each team wants to maximize the total power of its heroes. However, there is one exception: there are m pairs of heroes that are especially strong against each other, so when any team chooses a hero from such a pair, the other team must choose the other one on its turn. Each hero is in at most one such pair.

This is an interactive problem. You are to write a program that will optimally choose the heroes for one team, while the jury's program will play for the other team. Note that the jury's program may behave inefficiently, in this case you have to take the opportunity and still maximize the total power of your team. Formally, if you ever have chance to reach the total power of q or greater regardless of jury's program choices, you must get q or greater to pass a test.

Input

The first line contains two integers n and m (1 ≤ n ≤ 10^3, 0 ≤ m ≤ n) — the number of players in one team and the number of special pairs of heroes.

The second line contains 2n integers p_1, p_2, …, p_{2n} (1 ≤ p_i ≤ 10^3) — the powers of the heroes.

Each of the next m lines contains two integer a and b (1 ≤ a, b ≤ 2n, a ≠ b) — a pair of heroes that are especially strong against each other. It is guaranteed that each hero appears at most once in this list.

The next line contains a single integer t (1 ≤ t ≤ 2) — the team you are to play for. If t = 1, the first turn is yours, otherwise you have the second turn.

Hacks

In order to hack, use the format described above with one additional line. In this line output 2n distinct integers from 1 to 2n — the priority order for the jury's team. The jury's team will on each turn select the first possible hero from this list. Here possible means that it is not yet taken and does not contradict the rules about special pair of heroes.

Interaction

When it is your turn, print a single integer x (1 ≤ x ≤ 2n) — the index of the hero chosen by you. Note that you can't choose a hero previously chosen by either you of the other player, and you must follow the rules about special pairs of heroes.

When it is the other team's turn, read a line containing a single integer x (1 ≤ x ≤ 2n) — the index of the hero chosen by the other team. It is guaranteed that this index is not chosen before and that the other team also follows the rules about special pairs of heroes.

After the last turn you should terminate without printing anything.

After printing your choice do not forget to output end of line and flush the output. Otherwise you will get Idleness limit exceeded. To do this, use:

  * fflush(stdout) or cout.flush() in C++;
  * System.out.flush() in Java;
  * flush(output) in Pascal;
  * stdout.flush() in Python;
  * see documentation for other languages.



Jury's answer -1 instead of a valid choice means that you made an invalid turn. Exit immediately after receiving -1 and you will see Wrong answer verdict. Otherwise you can get an arbitrary verdict because your solution will continue to read from a closed stream.

Examples

Input


3 1
1 2 3 4 5 6
2 6
1

2

4

1


Output






6

5

3


Input


3 1
1 2 3 4 5 6
1 5
2
6

1

3


Output







5

4

2

Note

In the first example the first turn is yours. In example, you choose 6, the other team is forced to reply with 2. You choose 5, the other team chooses 4. Finally, you choose 3 and the other team choose 1.

In the second example you have the second turn. The other team chooses 6, you choose 5, forcing the other team to choose 1. Now you choose 4, the other team chooses 3 and you choose 2.

Solution (in JAVA):

Solution:
 import java.io.*;
import java.util.*;
import java.text.*;
import java.lang.*;
import java.lang.reflect.Array;
import java.math.BigInteger;
import java.util.regex.*;
public class Main {
          // public static ArrayList a[]=new ArrayList[300001];
           static boolean visited[]=new boolean[3000001];
           static int a[][];
           static  int chk(int x,int y) {
        	   if(a[y][0]==x || a[y][1]==x)
        		   return y;
        	   else
        		   return x;
           }
			public static void main(String[] args) 
	        {
	            InputReader in = new InputReader(System.in);
	            PrintWriter pw = new PrintWriter(System.out);
	            int n=in.nextInt();
	            int m=in.nextInt();
	            pair a[]=new pair[2*n];
	            long value[]=new long[2*n+1];
	            int p[]=new int[2*n+1];
	            for(int i=1;i<=2*n;i++)
	            {
	            	a[i-1]=new pair(in.nextLong(),i,-1);
	            	value[i]=a[i-1].x;
	            }
	            Vector<Integer>v=new Vector<>();
	            for(int i=0;i<m;i++) {
	            	int x=in.nextInt();
	            	int y=in.nextInt();
	            	p[x]=y;
	            	p[y]=x;
	            	v.add(value[x]>value[y]?x:y);
	            }
	            Arrays.sort(a);
	            int t=in.nextInt();
	            if(t==1) {
	            	int idx=0;
	            	while(idx<v.size()) {
	            		pw.println(v.get(idx));
	            		pw.flush();
	            		visited[v.get(idx)]=true;
	            		int x=in.nextInt();
	            		visited[x]=true;
	            		idx++;
	            	}
	            	int i=2*n-1;
	            	while(i>=0) {
	            		while(i>=0 &&visited[a[i].y]) {
	            			i--;
	            		}
	            		if(i<0)
	            			break;
	            		visited[a[i].y]=true;
	            		pw.println(a[i].y);
	            		pw.flush();
	            		int x=in.nextInt();
	            		visited[x]=true;
	            	}
	            	
	            }
	            else
	            {
	            	int idx=0;
	            	int id=2*n-1;
	            	for(int i=0;i<n;i++){
		            	int x=in.nextInt();
		            	visited[x]=true;
		            	if(p[x]!=0 && !visited[p[x]]) {
		            		pw.println(p[x]);
		            		pw.flush();
		            		visited[p[x]]=true;
		            	}
		            	else
		            	{
		            		while(idx<v.size() && visited[v.get(idx)]) {
		            			idx++;
		            		}
		            	    if(idx==v.size()) {
		            	    	while(visited[a[id].y]) {
		            	    		id--;
		            	    	}
		            	    	if(id<0)
		            	    		break;
		            	    	visited[a[id].y]=true;
		            	    	pw.println(a[id].y);
		            	    	pw.flush();
		            	    }
		            	    else
		            	    {
		            	    	pw.println(v.get(idx));
		            	    	pw.flush();
		            	    	visited[v.get(idx)]=true;
		            	    	idx++;
		            	    }
		            	}
	            	}
	            }
	            pw.flush();
	            pw.close();
	        
	        }
		private static void debug(Object... o) {
			System.out.println(Arrays.deepToString(o));
		}
		static class trie{
			
			Integer cnt;
			trie a[];
			trie(){
				cnt=0;
			    a=new trie[2];
			}
			
		}
        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;
        }
        static class tri implements Comparable<tri> {
            int p, c, l;
 
            tri(int p, int c, int l) {
                this.p = p;
                this.c = c;
                this.l = l;
            }
 
            public int compareTo(tri o) {
                return Integer.compare(l, o.l);
            }
        }
 
        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 long d;
        //public static long p;
        public static long 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 int primeFactorization(int n)
        {
            HashSet<Integer> a =new HashSet<Integer>();
            int ans=Integer.MIN_VALUE;
            for(int i=2;i*i<=n;i++)
            {
                while(n%i==0)
                {
                    ans=Math.max(ans, i);
                    n/=i;
                }
            }
            if(n!=1)
            	ans=Math.max(ans, n);
            return ans;
        }
        
        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(long d1,long d2)
        {
            if(d2==0)
            {
                d = d1;
             //   p = 1 ;
                q = 0;
            }
            else
            {
                extendedEuclid(d2, d1%d2);
             //   long temp = p;
              //  p = q;
                //q = temp - (d1/d2)*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%M*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%M * x%M)%M;
                x=(x%M * x%M)%M;
                n=n/2;
            }
            return result;
        }
        
        public static long 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;
        }
        
         public static pair[] shuffle(pair[] t, Random gen){ 
                for(int i = 0, n = t.length;i < n;i++){ 
                    int ind = gen.nextInt(n-i)+i; 
                    pair d = t[i]; 
                    t[i] = t[ind]; 
                    t[ind] = d; 
                } 
                return t; 
            }
        static class pair implements Comparable<pair>
        {
            Long x;
            Integer y;
            Integer z;
            pair(long a,int w,int z)
            {
                this.x=a;
                this.y=w;
                this.z=z;
            }
 

 
 
 
 
 
        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+" "+z;
            }
            
            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();
            }
        }
        
}