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.util.*;
import java.io.BufferedInputStream;
import java.math.*;
import static java.lang.Math.*;
import static java.lang.Character.*;
public class Main{
	public static void main(String[]args){
		B545 a=new B545();
		a.solve();
	}
}

class A96{
	private Scanner input=new Scanner(new BufferedInputStream(System.in));
	public void solve(){
		while(input.hasNext()){
			String s=input.next();
			s=s.replaceAll("0000000","*");
			s=s.replaceAll("1111111","*");
			if(s.contains("*"))System.out.println("YES");
			else System.out.println("NO");
		}
	}
}

class A112{
	private Scanner input=new Scanner(new BufferedInputStream(System.in));
	public void solve(){
		String a=input.nextLine();
		String b=input.nextLine();
		if(a.compareToIgnoreCase(b)<0)System.out.println(-1);
		else if(a.compareToIgnoreCase(b)==0)System.out.println(0);
		else System.out.println(1);
	}
}

class A339{
	private Scanner input=new Scanner(new BufferedInputStream(System.in));
	public void solve(){
		int []a=new int[1000];
		String s=input.nextLine();
		int t=0;
		for(int i=0;i<s.length();i++){
			if(Character.isDigit(s.charAt(i))){
				a[t++]=s.charAt(i)-'0';
			}
		}
		Arrays.sort(a,0,t);
		for(int i=0;i<t-1;i++){
			System.out.print(a[i]+"+");
		}
		System.out.println(a[t-1]);
	}
}

class B508{
	private Scanner input=new Scanner(new BufferedInputStream(System.in));
	public void solve(){
		StringBuilder s;
		s=new StringBuilder(input.nextLine());
		boolean ok=false;
		int n=s.length();
		int m=s.charAt(n-1)-'0';
		for(int i=0;i<n;i++){
			if(ok)break;
			int t=s.charAt(i)-'0';
			if(t%2==0&&t<m){
				Character tc=s.charAt(i);
				s.setCharAt(i,s.charAt(n-1));
				s.setCharAt(n-1,tc);
				ok=true;
			}
		}

		if(ok){
			System.out.println(s);
		}
		else {
			for(int i=n-2;i>=0;i--){
				int t=s.charAt(i)-'0';
				if(t%2==0){
					Character tc=s.charAt(i);
					s.setCharAt(i,s.charAt(n-1));
					s.setCharAt(n-1,tc);
					ok=true;
					break;
				}
			}
			if(ok)System.out.println(s);
			else System.out.println(-1);
		}
	}
}

class A352{
	Scanner input=new Scanner(new BufferedInputStream(System.in));
	public void solve(){
		int n=input.nextInt();
		int t,t5=0,t0=0;
		for(int i=0;i<n;i++){
			t=input.nextInt();
			if(t==5)t5++;
			if(t==0)t0++;
		}
		if(t0==0)System.out.println(-1);
		else if(t5>=9){
			int tt=t5/9;
			while(tt-->0)
				for(int i=0;i<9;i++)System.out.print(5);
			for(int i=0;i<t0;i++)System.out.print(0);
			System.out.println();
		}
		else System.out.println(0);
	}
}

class A629{
	private Scanner input=new Scanner(new BufferedInputStream(System.in));
	private int [][]a=new int[105][105];
	private String []s=new String[105];

	public void solve(){
		int n=input.nextInt();
		input.nextLine();
		for(int i=0;i<n;i++){
			s[i]=input.nextLine();
			Arrays.fill(a[i],0);
		}
		for(int i=0;i<n;i++){
			for(int j=0;j<n;j++){
				if(s[i].charAt(j)=='C'){
					a[i][n]++;
					a[n][j]++;
				}
			}
		}
		int ans=0;
		for(int i=0;i<n;i++){
			ans+=a[i][n]*(a[i][n]-1)/2;
			ans+=a[n][i]*(a[n][i]-1)/2;
		}
		System.out.println(ans);
	}
}

class A320{
	private Scanner input=new Scanner(new BufferedInputStream(System.in));

	public void solve(){
		String s=input.nextLine();
		s=s.replaceAll("[^14]","&");
		s=s.replaceAll("144","---");
		s=s.replaceAll("14","--");
		s=s.replaceAll("1","-");
		s=s.replaceAll("[-]","");
		if(s.length()==0)System.out.println("YES");
		else System.out.println("NO");
	}
}

class A38{
	private Scanner input=new Scanner(new BufferedInputStream(System.in));

	public void solve(){
		int n=input.nextInt();
		int []a=new int[105];
		for(int i=0;i<n-1;i++){
			a[i]=input.nextInt();
		}
		int s=input.nextInt();
		int b=input.nextInt();
		int ans=0;
		for(int i=s-1;i<b-1;i++){
			ans+=a[i];
		}
		System.out.println(ans);
	}
}

class A262{
	private Scanner input=new Scanner(new BufferedInputStream(System.in));

	public void solve(){
		int n=input.nextInt();
		int k=input.nextInt();
		int ans=0;
		for(int i=0;i<n;i++){
			Integer a=input.nextInt();
			String s=a.toString();
			int t=0;
			for(int j=0;j<s.length();j++){
				if(s.charAt(j)=='4'||s.charAt(j)=='7')t++;
			}
			if(t<=k)ans++;
		}
		System.out.println(ans);
	}
}

class A525{
	private Scanner input=new Scanner(new BufferedInputStream(System.in));
	private int []key=new int[27];

	public void solve(){
		int ans=0;
		Arrays.fill(key,0);
		int n=input.nextInt();
		input.nextLine();
		String s=input.nextLine();
		for(int i=0;i<s.length();i++){
			if(isUpperCase(s.charAt(i))){
				int tk=s.charAt(i)-'A';
				if(key[tk]>0)key[tk]--;
				else ans++;
			}
			else if(isLowerCase(s.charAt(i))){
				int tk=s.charAt(i)-'a';
				key[tk]++;
			}
		}
		System.out.println(ans);

	}
}

class B545{
	private Scanner input=new Scanner(new BufferedInputStream(System.in));

	public void solve(){
		
		String s1=input.nextLine();
		String s2=input.nextLine();
		StringBuilder s=new StringBuilder("");
		int same=0,dif=0,n=s1.length();
		int a=0,b=0;
		for(int i=0;i<n;i++){
			s.append(" ");
			if(s1.charAt(i)==s2.charAt(i)){
				same++;
				s.setCharAt(i,'1');
			}
			else {
				dif++;
				if(a<=b){
					if(s1.charAt(i)=='1')s.setCharAt(i,'0');
					else s.setCharAt(i,'1');
					a++;
				}
				else {
					if(s2.charAt(i)=='1')s.setCharAt(i,'0');
					else s.setCharAt(i,'1');
					b++;
				}
			}
		}

		if(dif%2==1)System.out.println("impossible");
		else System.out.println(s);
	}
}