Problem: Marina loves strings of the same length and Vasya loves when there is a third string, different from them in exactly t characters. Help Vasya find at least one such string.

More formally, you are given two strings s1, s2 of length n and number t. Let's denote as f(a, b) the number of characters in which strings a and b are different. Then your task will be to find any string s3 of length n, such that f(s1, s3) = f(s2, s3) = t. If there is no such string, print  - 1.

Input

The first line contains two integers n and t (1 ≤ n ≤ 105, 0 ≤ t ≤ n).

The second line contains string s1 of length n, consisting of lowercase English letters.

The third line contain string s2 of length n, consisting of lowercase English letters.

Output

Print a string of length n, differing from string s1 and from s2 in exactly t characters. Your string should consist only from lowercase English letters. If such string doesn't exist, print -1.

Examples

Input

3 2
abc
xyc


Output

ayd

Input

1 0
c
b


Output

-1

Solution (in JAVA):

Solution:
import java.util.*;

public class Main {
  Scanner sc;

  void run() {
    int n = ni();
    int t = ni();
    char[] s1 = sc.next().toCharArray();
    char[] s2 = sc.next().toCharArray();
    boolean[] bits = new boolean[ n ];

    int count = 0;
    for ( int i = 0; i < n; ++i ) {
      if ( s1[ i ] != s2[ i ] ) {
        ++count;
      }
      bits[ i ] = s1[ i ] == s2[ i ];
    }
    if ( (count + 1) / 2 > t ) {
      System.out.println(-1);
      return;
    }

    char[] s3 = s1.clone();
    for ( int i = 0; i < n; ++i ) {
      if ( !bits[ i ] ) {
        char c = 'a';
        while ( s1[ i ] == c || s2[ i ] == c ) {
          c = (char) (c + 1);
        }
        s3[ i ] = c;
        --t;
      }
    }

    //debug(t, s3);

    int idx = 0;
    while ( t < 0 && idx < n ) {
      for ( int i = 0; i < 2; ++i ) {
        for (; idx < n; ++idx ) {
          if ( !bits[ idx ] ) {
            if ( i == 0 ) {
              s3[ idx ] = s1[ idx ];
            } else {
              s3[ idx ] = s2[ idx ];
            }
            ++idx;
            break;
          }
        }
      }
      t += 1;
    }

    for ( int i = 0; i < n && t > 0; ++i ) {
      if ( bits[ i ] ) {
        char c = 'a';
        while ( s1[ i ] == c || s2[ i ] == c ) {
          c = (char) (c + 1);
        }
        s3[ i ] = c;
        --t;
      }
    }

    System.out.println(new String(s3));
  }

  Main() {
    sc = new Scanner(System.in);
  }

  int ni() {
    return sc.nextInt();
  }

  public static void main(String[] args) {
    new Main().run();
  }

  void debug(Object... os) {
    System.err.println(Arrays.deepToString(os));
  }
}