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.util.*;


// http://codeforces.com/contest/8/problem/D

public class Main {
	
	static double epsion = 0.000000001;
	static double unit = 0.000001 ;
	static point cinema,house,shop;
	static double total1,total2;
	
	public static void main(String args[] ) throws Exception {

		Scanner sc = new Scanner( System.in );
		
 		String s1 = sc.next();
		String s2 = sc.next();

		StringBuilder sb = new StringBuilder( s1);
		
		int c1 = 0 , c2 = 0 ;
		
		int n  = s1.length();
		
		for( int i = 0 ; i < n ; ++i ){
			
			if( s1.charAt(i) == s2.charAt(i)){
				
				sb.setCharAt(i, s1.charAt(i));
				continue;
			}
			
			
			if( c1 > c2 ) {
				
				sb.setCharAt(i, s2.charAt(i));
				c2++;
			}
			
			else{
				
				sb.setCharAt(i, s1.charAt(i));
				c1++;
			}
		}
		
		if( c1 != c2 ){
			System.out.println("impossible");
		}
		
		else{
			
			System.out.println(sb.toString());
		}
	}

	static boolean possible( double x ){
		
		boolean ans = false;
		ans = ans || check(cinema,x,shop,total1 - x - distance(shop,house),house,total2-x);
		ans = ans || check(cinema,x,house,total2-x,shop,total1 - x - distance(shop,house));
		ans = ans || check(shop,total1 - x - distance(shop,house),house,total2-x,cinema,x);
		
		//ans = ans || check2(cinema,x,shop,total1 - x - distance(shop,house),house,total2-x);
		
		return ans;
	}
	
	static boolean check( point p1 , double r1 , point p2 , double r2 , point p3, double r3 ){
		// intersect first and second , and check third then
		double d = distance(p1,p2);
		double a = (r1*r1 - r2*r2 + d*d)/(2*d);
		// a = distance between p1 and mid
		double dy = p2.y - p1.y;
		double dx = p2.x - p1.x ; 
		double xmid,ymid;
		xmid = p1.x + (dx*a)/d;
		ymid = p1.y + (dy*a)/d;
		
		double h = Math.sqrt((r1*r1 - a*a));
		double rx = -(h * dy)/d;
		double ry = (h*dx)/d;
		
		if( inside(xmid+rx,ymid+ry,p3,r3) || inside(xmid-rx,ymid-ry,p3,r3) )
			return true;
		
		else
			return false;
	}
	

	static boolean check2( point p1 , double r1 , point p2 , double r2 , point p3, double r3 ){
		// intersect first and second , and check third then
		circle[] array = new circle[3];
		
		array[0] = new circle(p1,r1);
		array[1] = new circle(p2,r2);
		array[2] = new circle(p3,r3);
		
		Arrays.sort( array );
		
		if( engulfs( array[2],array[1]) && engulfs( array[3],array[0]) )
		return true;
		
		else return false;
	}
	
	static boolean engulfs( circle outer, circle inner){
		
		if( outer.radius > inner.radius + distance(outer.center,inner.center))
		return true;
		
		else
			return false;
	}
	
	static class circle implements Comparable<circle>{
		
		point center;
		double radius;
		
		circle( point p , double r){
			center = p;
			radius = r;
		}
		
		public int compareTo(circle c){
			if( radius < c.radius ) return -1;
			else if( radius > c.radius ) return +1;
			else return 0;
		}
	}
	static boolean inside( double x , double y , point p , double r ){
	
		if( (x-p.x)*(x-p.x) + (y - p.y)*(y-p.y) <= r*r ) return true; 
		else return false;
		
	}
	
	static double distance( point p1, point p2){
		
		return Math.sqrt(  (p1.x - p2.x)*(p1.x - p2.x) + (p1.y - p2.y)*(p1.y - p2.y) ) ;
	}

	static class point{
		
		int x,y;
		point(int x,int y){
			this.x = x;
			this.y = y;
		}
	}  	
	
	static class IO{
		
		
		BufferedReader reader;
		StringTokenizer tokenizer;
		PrintWriter writer;

		public void init() {
			try {
				reader = new BufferedReader(new InputStreamReader(System.in),8*1024);
				writer = new PrintWriter(System.out);
			} catch (Exception e) {
				e.printStackTrace();
				System.exit(261);
			}
		}

		void destroy() {
			writer.close();
			System.exit(0);
		}

		void print(Object... objects) {
			for (int i = 0; i < objects.length; i++) {
				if (i != 0)
					writer.print(' ');
				writer.print(objects[i]);
			}
		}

		void println(Object... objects) {
			print(objects);
			writer.println();
		}

		String nextLine() throws IOException {
			return reader.readLine();
		}

		String nextToken() throws IOException {
			while (tokenizer == null || !tokenizer.hasMoreTokens())
				tokenizer = new StringTokenizer(nextLine());
			return tokenizer.nextToken();
		}

		int nextInt() throws NumberFormatException, IOException {
			return Integer.parseInt(nextToken());
		}

		long nextLong() throws NumberFormatException, IOException {
			return Long.parseLong(nextToken());
		}

		double nextDouble() throws NumberFormatException, IOException {
			return Double.parseDouble(nextToken());
		}
	}
	
	
	
}

/*
0 2
0 0
40 0
-31 1

1.0002538218


 */