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.math.BigInteger;
		import java.util.*;
			
			
			public class Practice {
				private static InputStream stream;
				private static byte[] buf = new byte[1024];
				private static int curChar;
				private static int numChars;
				private static SpaceCharFilter filter;
				private static PrintWriter pw;
				private static long mod=1000000007;
			
			    public static void main(String[] args) {
			    	InputReader(System.in);
					pw = new PrintWriter(System.out); 
			        new Thread(null ,new Runnable(){
			           public void run(){
			               try{
			                   solve();//This is solution method
		               pw.close();
		           } catch(Exception e){
		               e.printStackTrace();
		           }
		       }
		   },"1",1<<26).start();
			    				   }
			    				    static long sort(int a[])
			        		    	{  int n=a.length;
			        		    		int b[]=new int[n];	
			        		    		return mergeSort(a,b,0,n-1);}
			        		    	static long mergeSort(int a[],int b[],long left,long right)
			        		    	{ long c=0;if(left<right)
			        		    	 {   long mid=left+(right-left)/2;
			        		    		 c= mergeSort(a,b,left,mid);
			        		    		 c+=mergeSort(a,b,mid+1,right);
			        		    		 c+=merge(a,b,left,mid+1,right); }	
			        		    		return c;	 }
			        		    	static long merge(int a[],int  b[],long left,long mid,long right)
			        		    	{long c=0;int i=(int)left;int j=(int)mid; int k=(int)left;
			        		    	while(i<=(int)mid-1&&j<=(int)right)
			        		    	{ if(a[i]>a[j]) {b[k++]=a[i++]; }
			        		    	else	{ b[k++]=a[j++];c+=mid-i;}}
			        		    	while (i <= (int)mid - 1)   b[k++] = a[i++]; 
			        		    	while (j <= (int)right) b[k++] = a[j++];
			        		    	for (i=(int)left; i <= (int)right; i++) 
			        		    		a[i] = b[i];  return c;  }
			        		    		    
			    				    
	    				    
	        		    	public static void solve() {
	        	
	        		    		String s=nextLine();
	        		    		String t=nextLine();
	        		    		int diff=0;
	        		    		for(int i=0;i<s.length();i++){
	        		    			if(s.charAt(i)!=t.charAt(i)){
	        		    				diff++;
	        		    			}
	        		    		}
	        		    		if(diff%2!=0){
	        		    			pw.println("impossible");
	        		    		return ;
	        		    		}
	        		    		
	        		    		int count=1;
	        		    		for(int i=0;i<s.length();i++){
	        		    			if(s.charAt(i)!=t.charAt(i)){
	        		    				if(count%2!=0){
	        		    					pw.print(s.charAt(i));
	        		    				}else{
	        		    					pw.print(t.charAt(i));
	        		    				}
	        		    				count++;
	        		    			}else{
	        		    				pw.print(s.charAt(i));
	        		    			}
	        		    		}
	        		    	}
        		    		
		        		    		
		        		    				
		        		        
		public static boolean isVowel(char c){        		    		
			if(c=='a' || c=='i'|| c=='e' || c=='o' || c=='u')
					return true;
				return false;
			}
			
			public static long trailingZeroes(long n) {
			    long count = 0;
		
			    while (n > 0) {
			        n /= 5;
			        count += n;
			    }
		
			    return count;
			}
		
		    public static int largestPrimeFactor(long number) {
		        int i;
		
		        for (i = 2; i <= number; i++) {
		            if (number % i == 0) {
		                number /= i;
		                i--;
		            }
		        }
		
		        return i;
		}
		   
			
		    public static String reverseString(String s) {
				StringBuilder sb = new StringBuilder(s);
				sb.reverse();
				return (sb.toString());
			}
		    private static BigInteger ncr(int n,int k){
		    	if (k < 0 || k > n) return BigInteger.ZERO;
		        if (n-k < k) k = n-k;
		
		        BigInteger x = BigInteger.ONE;
		        for (int i = 1; i <= k; i++) {
		            x = x.multiply(new BigInteger(""+(n-i+1)));
		x = x.divide(new BigInteger(""+i));
		        }
		
		return x;
		    }
		    static long fact[];
		private static void factmod(int n,int mod){
			fact=new long[n+1];
			fact[0]=1;
			for(int i=1;i<=n;i++){
				fact[i]=i*fact[i-1];
				//fact[i]%=mod;
		
			}
			
		}
		private static long phi(long n){
			long ans=n;
			if(n%2==0)
				ans-=(ans/2);
			while(n%2==0)
			{
				n/=2;
				
			}
			for(int i=3;i*i<=n;i+=2){
				if(n%i==0){
				while(n%i==0){
					n/=i;
				}
				ans-=(ans/i);
				}
			}
			if(n>2)
				ans-=(ans/n);
			
			return ans;
		}
		static long d,x,y;
		static long modInverse(long A, long M)
		{
		extendedEuclid(A,M);
		return (x%M+M)%M;    //x may be negative
		}
		static void extendedEuclid(long A, long B) {
		if(B == 0) {
		d = A;
		x = 1;
		y = 0;
		}
		else {
		extendedEuclid(B, A%B);
		long temp = x;
		x = y;
		y = temp - (A/B)*y;
		}
		}
		static boolean prime[];
		static int spf[];
		public static void sieve(int n){
			prime=new boolean[n+1];
			spf=new int[n+1];
			
			Arrays.fill(spf, 1);
			Arrays.fill(prime, true);
		prime[1]=false;
			spf[2]=2;
			for(int i=4;i<=n;i+=2)
			{
				spf[i]=2;
				prime[i]=false;
			}
		
		for(int i=3;i<=n;i+=2){
			if(prime[i]){
				spf[i]=i;
				for(int j=2*i;j<=n;j+=i){
					
					prime[j]=false;
				if(spf[j]==1){
					spf[j]=i;
				}
				}
			}
		}
			
		}
		public static boolean isPrime(long n) {
			
			if (n <= 1)
				return false;
			if (n <= 3)
				return true;
		
			if (n % 2 == 0 || n % 3 == 0)
				return false;
		
			for (long i = 5; i * i <= n; i = i + 6)
				if (n % i == 0 || n % (i + 2) == 0)
					return false;
		
			return true;
		}
		
		    public static long pow(long n, long p,long mod) {
				if(p==0)
					return 1;
				if(p==1)
					return n%mod;
				if(p%2==0){
					long temp=pow(n, p/2,mod);
				return (temp*temp)%mod;
				}else{
					 	long temp=pow(n,p/2,mod);
					 	temp=(temp*temp)%mod;
					 	return(temp*n)%mod;
					 	
				}
			}
			public static long gcd(long x, long y) {
				if (x == 0)
					return y;
				else
					return gcd( y % x,x);
			}
			
			
			public static void InputReader(InputStream stream1) {
				stream = stream1;
			}
		 
			private static boolean isWhitespace(int c) {
				return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
			}
		 
			private static boolean isEndOfLine(int c) {
				return c == '\n' || c == '\r' || c == -1;
			}
		 
			private static 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++];
			}
		 
			private static 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;
			}
		 
			private static 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;
			}
		 
			private static String nextToken() {
				int c = read();
				while (isSpaceChar(c))
					c = read();
				StringBuilder res = new StringBuilder();
				do {
					res.appendCodePoint(c);
					c = read();
				} while (!isSpaceChar(c));
				return res.toString();
			}
		 
			private static String nextLine() {
				int c = read();
				while (isSpaceChar(c))
					c = read();
				StringBuilder res = new StringBuilder();
				do {
					res.appendCodePoint(c);
					c = read();
				} while (!isEndOfLine(c));
				return res.toString();
			}
		 
			private static int[] nextIntArray(int n) {
				int[] arr = new int[n];
				for (int i = 0; i < n; i++) {
					arr[i] = nextInt();
				}
				return arr;
			}
		 
			private static int[][] next2dArray(int n, int m) {
				int[][] arr = new int[n][m];
				for (int i = 0; i < n; i++) {
					for (int j = 0; j < m; j++) {
						arr[i][j] = nextInt();
					}
				}
				return arr;
			}
			private static char[][] nextCharArray(int n,int m){
				char [][]c=new char[n][m];
				for(int i=0;i<n;i++){
					String s=nextLine();
					for(int j=0;j<s.length();j++){
						c[i][j]=s.charAt(j);
					}
				}
				return c;
			}
		 
			private static long[] nextLongArray(int n) {
				long[] arr = new long[n];
				for (int i = 0; i < n; i++) {
					arr[i] = nextLong();
				}
				return arr;
			}
		 
			private static void pArray(int[] arr) {
				for (int i = 0; i < arr.length; i++) {
					pw.print(arr[i] + " ");
				}
				pw.println();
				return;
			}
		 
			private static void pArray(long[] arr) {
				for (int i = 0; i < arr.length; i++) {
					pw.print(arr[i] + " ");
				}
				pw.println();
				return;
			}
		 
			private static void pArray(boolean[] arr) {
				for (int i = 0; i < arr.length; i++) {
					pw.print(arr[i] + " ");
				}
				pw.println();
				return;
			}
		 
			private static boolean isSpaceChar(int c) {
				if (filter != null)
					return filter.isSpaceChar(c);
				return isWhitespace(c);
			}
		 
			private interface SpaceCharFilter {
				public boolean isSpaceChar(int ch);
			}
		
			
		}	
		
	/*class Pair implements Comparable<Pair>{
		
			
			int  bea,pri;
			Pair(int bea,int pri){
			
				this.bea=bea;
				this.pri=pri;
				
			}
			@Override
			public int compareTo(Pair o) {
		
				return 0;
				//return (int)(o.size-size);
			}
			public int hashCode() {
					//int hu = (int) (x ^ (x >>> 32));
					//int hv = (int) (y ^ (y >>> 32));
					//int hw = (int) (mass ^ (mass >>> 32));
					//return 31 * hu + hv ;
				return 0;
				}
				public boolean equals(Object o) {
					Pair other = (Pair) o;
				//	return x == other.x && y == other.y;
				return false;
				}
		}
		*/