Problem: Little Susie loves strings. Today she calculates distances between them. As Susie is a small girl after all, her strings contain only digits zero and one. She uses the definition of Hamming distance:

We will define the distance between two strings s and t of the same length consisting of digits zero and one as the number of positions i, such that si isn't equal to ti. 

As besides everything else Susie loves symmetry, she wants to find for two strings s and t of length n such string p of length n, that the distance from p to s was equal to the distance from p to t.

It's time for Susie to go to bed, help her find such string p or state that it is impossible.

Input

The first line contains string s of length n. 

The second line contains string t of length n.

The length of string n is within range from 1 to 105. It is guaranteed that both strings contain only digits zero and one.

Output

Print a string of length n, consisting of digits zero and one, that meets the problem statement. If no such string exist, print on a single line "impossible" (without the quotes).

If there are multiple possible answers, print any of them.

Examples

Input

0001
1011


Output

0011


Input

000
111


Output

impossible

Note

In the first sample different answers are possible, namely — 0010, 0011, 0110, 0111, 1000, 1001, 1100, 1101.

Solution (in JAVA):

Solution:
    import java.io.*;
    import java.lang.reflect.Array;
    import java.math.BigInteger;
    import java.util.*;
    import java.lang.*;
    import static java.lang.Math.*;
    public class main implements Runnable {

        public static void main(String[] args) {
            new Thread(null, new main(), "Check2", 1 << 28).start();// to increse stack size in java
        }
        void init(ArrayList <Integer> adj[], int n){
            for(int i=0;i<=n;i++)adj[i]=new ArrayList<>();
        }
        static long mod = (long) (1e9 + 7);
        public void run() {
            InputReader in = new InputReader(System.in);
            PrintWriter w = new PrintWriter(System.out);

            char c[]=in.next().toCharArray();
            char d[]=in.next().toCharArray();
            char e[]=new char[c.length];
            int co=0;

            for(int i=0;i<c.length;i++){
                if(c[i]!=d[i]){
                    if(co%2==0)e[i]=c[i];
                    else e[i]=d[i];
                    co++;
                }
                else{
                    e[i]='1';
                }

            }
            if(co%2!=0){
                w.println("impossible");
            }
            else
                w.println(String.valueOf(e));



            w.close();
        }

        class pair2 implements  Comparable <pair2>{
            String a;
            int b;
            pair2(String a,int b){
                this.a=a;
                this.b=b;
            }
            public  int compareTo(pair2 o){
                return -(this.b-o.b);

            }
        }

        static void diji(int s, long dist[], ArrayList<pair> adj[]) {
            dist[s] = 0;
            PriorityQueue<pair> q = new PriorityQueue<>(new cmp());
            q.add(new pair(s, 0));
            while (!q.isEmpty()) {
                pair p1 = q.poll();
                for (pair ne: adj[p1.a]) {

                    if ((long) p1.b + (long) ne.b < dist[ne.a]) {
                        dist[ne.a] = (long) p1.b + (long) ne.b;
                        pair p2 = new pair(ne.a, dist[ne.a]);
                        q.add(p2);

                    }

                }
            }

        }
        static class cmp implements Comparator<pair>{

            public  int compare(pair o1,pair o2)
            {
                return o1.b<o2.b?-1:o1.b>o2.b?1:0;
            }

        }

        static class pair {
            int a;
            long b;
            pair(int a,long b){
                this.a=a;
                this.b=b;
            }
            public boolean equals(Object obj) {      //  override equals method for object to remove tem from arraylist and sets etc.......
                if (this == obj)
                    return true;
                if (obj == null)
                    return false;
                if (getClass() != obj.getClass())
                    return false;
                pair other = (pair) obj;
                if (b!= other.b||a!=other.a)
                    return false;
                return true;
            }
        }

        static long modinv(long a,long b)
        {
            long p=power(b,mod-2);

            p=a%mod*p%mod;
            p%=mod;

            return p;

        }

        static long power(long x,long y){
            if(y==0)return 1%mod;
            if(y==1)return x%mod;


            long res=1;
            x=x%mod;
            while(y>0){


                if((y%2)!=0){
                    res=(res*x)%mod;
                }


                y=y/2;
                x=(x*x)%mod;
            }


            return res;

        }
        static  long gcd(long a,long b){

            if(b==0)return a;
            return gcd(b,a%b);
        }

        static  void sev(int a[],int n){

            for(int i=2;i<=n;i++)a[i]=i;
            for(int i=2;i<=n;i++){

                if(a[i]!=0){
                    for(int j=2*i;j<=n;){

                        a[j]=0;
                        j=j+i;
                    }
                }

            }

        }



        static class InputReader
        {
            private InputStream stream;
            private byte[] buf = new byte[1024];
            private int curChar;
            private int numChars;
            private SpaceCharFilter filter;

            public InputReader(InputStream stream)
            {
                this.stream = stream;
            }

            public int read()
            {
                if (numChars==-1)
                    throw new InputMismatchException();

                if (curChar >= numChars)
                {
                    curChar = 0;
                    try
                    {
                        numChars = stream.read(buf);
                    }
                    catch (IOException e)
                    {
                        throw new InputMismatchException();
                    }

                    if(numChars <= 0)
                        return -1;
                }
                return buf[curChar++];
            }

            public String nextLine()
            {
                BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
                String str = "";
                try
                {
                    str = br.readLine();
                }
                catch (IOException e)
                {
                    e.printStackTrace();
                }
                return str;
            }
            public int nextInt()
            {
                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;
            }

            public long nextLong()
            {
                int c = read();
                while (isSpaceChar(c))
                    c = read();
                int sgn = 1;
                if (c == '-')
                {
                    sgn = -1;
                    c = read();
                }
                long res = 0;

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

            public double nextDouble()
            {
                int c = read();
                while (isSpaceChar(c))
                    c = read();
                int sgn = 1;
                if (c == '-')
                {
                    sgn = -1;
                    c = read();
                }
                double res = 0;
                while (!isSpaceChar(c) && c != '.')
                {
                    if (c == 'e' || c == 'E')
                        return res * Math.pow(10, nextInt());
                    if (c < '0' || c > '9')
                        throw new InputMismatchException();
                    res *= 10;
                    res += c - '0';
                    c = read();
                }
                if (c == '.')
                {
                    c = read();
                    double m = 1;
                    while (!isSpaceChar(c))
                    {
                        if (c == 'e' || c == 'E')
                            return res * Math.pow(10, nextInt());
                        if (c < '0' || c > '9')
                            throw new InputMismatchException();
                        m /= 10;
                        res += (c - '0') * m;
                        c = read();
                    }
                }
                return res * sgn;
            }

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

            public String next()
            {
                return readString();
            }

            public interface SpaceCharFilter
            {
                public boolean isSpaceChar(int ch);
            }
        }







    }