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.BufferedWriter;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.io.Writer;
import java.util.InputMismatchException;

public final class Second
{
	private static int n;
	private static String s, t, p;
	private static InputReader reader;
	private static OutputWriter writer;
	
	public static void main(String[] args)
	{
		Second second = new Second();
		
		reader = second.new InputReader(System.in);
		writer = second.new OutputWriter(System.out);
		
		getAttributes();
		
		writer.flush();
		
		reader.close();
		writer.close();
	}
	
	public static void getAttributes()
	{
		s = reader.next();
		t = reader.next();
		
		n = s.length();
		
		int count = 0;
		
		for (int i = 0; i < n; i++)
		{
			if (s.charAt(i) != t.charAt(i))
				count++;
		}
		
		if (count % 2 == 0)
		{
			int a = 0;
			
			p = "";
			
			StringBuilder ans = new StringBuilder();
			
			ans.append(s);
			
			for (int i = 0; i < n; i++)
			{
				if (s.charAt(i) != t.charAt(i))
				{
					// System.out.println(s.charAt(i) + ", " + t.charAt(i));
					if (a % 2 == 0)
					{
						ans.setCharAt(i, t.charAt(i));
						// System.out.println("a : " + a + ", i : " + i + ", char : " + t.charAt(i));
					}
					
					a++;
					// System.out.println("a : " + a + ", count : " + count);
				}
			}
			
			writer.println(ans.toString());
			
/*			for (int i = 0; i < n; i++)
			{
				if (s.charAt(i) != t.charAt(i))
				{
					if (a % 2 == 0)
						p += s.charAt(i);
					else
						p += t.charAt(i);
					
					a++;
				}
				else
					p += s.charAt(i);
			}
			
			writer.println(p);*/
		}
		else
			writer.println("impossible");
	}
	
	class InputReader
	{
		private InputStream stream;
		private byte[] buf = new byte[1024];
		private int curChar;
		private int numChars;

		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 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 & 15;
				
				c = read();
			} while (!isSpaceChar(c));
			
			return res * sgn;
		}

		public long nextLong()
		{
			int c = read();
			
			while (isSpaceChar(c))
				c = read();
			
			int sign = 1;
			
			if (c == '-')
			{
				sign = -1;
				
				c = read();
			}
			
			long result = 0;
			
			do
			{
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				
				result *= 10;
				result += c & 15;
				
				c = read();
			} while (!isSpaceChar(c));
			
			return result * sign;
		}
		
		public float nextFloat() // problematic
		{
			float result, div;
			byte c;

			result = 0;
			div = 1;
			c = (byte) read();

			while (c <= ' ')
				c = (byte) read();

			boolean isNegative = (c == '-');

			if (isNegative)
				c = (byte) read();

			do
			{
				result = result * 10 + c - '0';
			} while ((c = (byte) read()) >= '0' && c <= '9');

			if (c == '.')
				while ((c = (byte) read()) >= '0' && c <= '9')
					result += (c - '0') / (div *= 10);

			if (isNegative)
				return -result;

			return result;
		}

		public double nextDouble() // not completely accurate
		{
			double ret = 0, div = 1;
			byte c = (byte) read();

			while (c <= ' ')
				c = (byte) read();

			boolean neg = (c == '-');

			if (neg)
				c = (byte) read();

			do
			{
				ret = ret * 10 + c - '0';
			} while ((c = (byte) read()) >= '0' && c <= '9');

			if (c == '.')
				while ((c = (byte) read()) >= '0' && c <= '9')
					ret += (c - '0') / (div *= 10);

			if (neg)
				return -ret;

			return ret;
		}

		public String next()
		{
			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)
		{
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}

		public void close()
		{
			try
			{
				stream.close();
			}
			catch (IOException e)
			{
				e.printStackTrace();
			}
		}

	}

	class OutputWriter
	{
		private PrintWriter writer;

		public OutputWriter(OutputStream stream)
		{
			writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(
					stream)));
		}

		public OutputWriter(Writer writer)
		{
			this.writer = new PrintWriter(writer);
		}

		public void println(int x)
		{
			writer.println(x);
		}

		public void print(int x)
		{
			writer.print(x);
		}
		
		public void println(int array[], int size)
		{
			for (int i = 0; i < size; i++)
				println(array[i]);
		}
		
		public void print(int array[], int size)
		{
			for (int i = 0; i < size; i++)
				print(array[i] + " ");
		}

		public void println(long x)
		{
			writer.println(x);
		}

		public void print(long x)
		{
			writer.print(x);
		}
		
		public void println(long array[], int size)
		{
			for (int i = 0; i < size; i++)
				println(array[i]);
		}
		
		public void print(long array[], int size)
		{
			for (int i = 0; i < size; i++)
				print(array[i]);
		}
		
		public void println(float num)
		{
			writer.println(num);
		}
		
		public void print(float num)
		{
			writer.print(num);
		}
		
		public void println(double num)
		{
			writer.println(num);
		}
		
		public void print(double num)
		{
			writer.print(num);
		}

		public void println(String s)
		{
			writer.println(s);
		}

		public void print(String s)
		{
			writer.print(s);
		}
		
		public void println()
		{
			writer.println();
		}

		public void printSpace()
		{
			writer.print(" ");
		}

		public void flush()
		{
			writer.flush();
		}

		public void close()
		{
			writer.close();
		}

	}

}