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.IOException;
import java.io.PrintWriter;
import java.util.Arrays;

public class CF2_303B {
  
  static Reader sc = new Reader();
  static PrintWriter out = new PrintWriter(System.out);
  
  public static void main(String[] args) throws IOException {
    char[] a = sc.next().toCharArray();
    char[] b = sc.next().toCharArray();
   
    int n = a.length;
    
    int countDif = 0;
    
    boolean[] dif = new boolean[n];
    
    for (int i = 0; i < n; i++) {
      if (a[i] != b[i]) {
        dif[i] = true;
        countDif++;
      }
    }
    
    if (countDif % 2 != 0) {
      out.println("impossible");
    } else {
      int left = countDif / 2;
      
      for (int i = 0; i < n; i++) {
        if(dif[i] && left > 0) {
          a[i] = b[i];
          left--;
        }
      }
      
      out.println(new String(a));
    }
    
    out.close();
  }
  
  static class Reader {
    final private int BUFFER_SIZE = 1 << 12; private byte[] buffer; private int bufferPointer, bytesRead; private boolean eof = false;
    public Reader() {buffer = new byte[BUFFER_SIZE];bufferPointer = bytesRead = 0;}
    public boolean reachedEOF() {return eof;}
    private void fillBuffer() throws IOException {bytesRead = System.in.read(buffer, bufferPointer = 0, BUFFER_SIZE); if (bytesRead == -1) { buffer[0] = -1;eof = true;}}
    private byte read() throws IOException {if (bufferPointer == bytesRead)fillBuffer();return buffer[bufferPointer++];}
    public String next() throws IOException {StringBuilder sb = new StringBuilder();byte c;while ((c = read()) <= ' ') {if (c == -1)return null;} do {sb.append((char) c);} while ((c = read()) > ' ');if (sb.length() == 0)return null;return sb.toString();}
    public String nextLine() throws IOException {StringBuilder sb = new StringBuilder();byte c;boolean read = false;while ((c = read()) != -1) {if (c == '\n') {read = true;break;}if (c >= ' ')sb.append((char) c);}if (!read)return null;return sb.toString();}
    public int nextInt() throws IOException {int ret = 0;byte c = read();while (c <= ' ')c = read();boolean neg = (c == '-');if (neg)c = read();do {ret = ret * 10 + c - '0';} while ((c = read()) >= '0' && c <= '9');if (neg)return -ret;return ret;}
    public long nextLong() throws IOException {long ret = 0;byte c = read();while (c <= ' ')c = read();boolean neg = (c == '-');if (neg)c = read();do {ret = ret * 10L + c - '0';} while ((c = read()) >= '0' && c <= '9');if (neg)return -ret;return ret;}
    public double nextDouble() throws IOException {double ret = 0, div = 1;byte c = read();while (c <= ' ')c = read();boolean neg = (c == '-');if (neg)c = read();do {ret = ret * 10 + c - '0';} while ((c = read()) >= '0' && c <= '9');if (c == '.')while ((c = read()) >= '0' && c <= '9')ret += (c - '0') / (div *= 10);if (neg)return -ret;return ret;}
    public int[] nextIntArray(int n) throws IOException {int[] a = new int[n];for (int i = 0; i < n; i++)a[i] = nextInt();return a;}
    public int[][] nextIntMatrix(int n, int m) throws IOException {int[][] map = new int[n][m];for (int i = 0; i < n; i++)map[i] = nextIntArray(m);return map;}
    public char[][] nextCharacterMatrix(int n) throws IOException {char[][] a = new char[n][];for (int i = 0; i < n; i++)a[i] = next().toCharArray();return a;}
    public void close() throws IOException {if (System.in == null)return;System.in.close();}
  }
  
  static void print(int[] A) {for(int i=0;i<A.length;i++){if(i!=0) out.print(' ');out.print(A[i]);}out.println();}
  static <T> void print(Iterable<T> A) {int i = 0;for(T act : A){if(i!=0)out.print(' ');out.print(act);i++;}out.println();}
  static void printPlus1(Iterable<Number> A) {int i = 0;for(Number act : A){if(i!=0)out.print(' ');out.print(act.longValue() + 1L);i++;}out.println();}
  static void debug(Object... o) { System.err.println(Arrays.deepToString(o)); }
  
  /*
    long s = System.currentTimeMillis();
    debug(System.currentTimeMillis()-s+"ms");
   */
}