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.io.*;
import java.io.PrintWriter;
import java.util.*;
import java.io.InputStream;
import java.io.DataInputStream;
 
 
 public class Main
{ 
   // static{ System.out.println("hello");}
        static InputStream inputStream = System.in;
        static OutputStream outputStream = System.out;
        static FastReader scn = new FastReader(inputStream);
        static PrintWriter out = new PrintWriter(outputStream);
      
         public static void main(String[] args) throws IOException
       { ArrayList<Character> ans=new ArrayList<Character>();
           int n=scn.ni();
         int t=scn.ni();  
          String s1=scn.ns();
          String s2=scn.ns();
          int a=n-t; int cnt=0;
          for(int i=0;i<n;i++)
          {
            if (s1.charAt(i)==s2.charAt(i)) cnt++;
                        
          }
         int cnt2=0; int first=0,second=0; int cnt3=0;
          if (cnt>=a)
          {     for(int i=0;i<n;i++)
              {   char ch1=s1.charAt(i);
                  char ch2=s2.charAt(i);
                  if (s1.charAt(i)==s2.charAt(i) && cnt2<a) 
                      { ans.add(s1.charAt(i)); cnt2++; }
                    else  
                      {   char new1=(char)((ch1+ch2)/2);
                          char new2=ch1 > ch2 ? ch2 :ch1;
                          char new3=ch1 > ch2 ? ch1 :ch2;
                          if (new2-1>97) ans.add((char)(new2-1));
                          else if (new3+1<122) ans.add((char)(new3+1));
                          else  ans.add(new1);
                        
                        }   
              }
              for(char ti: ans) out.print(ti); 
          }
          else
          {   int cnt4=0,cnt5=0; int temp=a-cnt;
              for(int i=0;i<n;i++)
                { char ch1=s1.charAt(i);
                  char ch2=s2.charAt(i);
                  if (s1.charAt(i)==s2.charAt(i) ) 
                      { ans.add(s1.charAt(i));}
                  else 
                    if (cnt4<temp) { ans.add(ch1); cnt4++; }  
                  else if (cnt5<temp)    { ans.add(ch2); cnt5++; } 
                   else  
                      {   char new1=(char)((ch1+ch2)/2);
                          char new2=ch1 > ch2 ? ch2 :ch1;
                          char new3=ch1 > ch2 ? ch1 :ch2;
                          if (new2-1>97) ans.add((char)(new2-1));
                          else if (new3+1<122) ans.add((char)(new3+1));
                          else  ans.add(new1);
                        
                        }   
                       
                } 
                if (cnt+cnt4==a && cnt+cnt5==a)  for(char ti: ans) out.print(ti); 
                else out.print(-1);
          }
         out.close();
        }    
                    
         
}


  class num implements Comparator<num>
    {
        
        public int ff;
        public int ss;
   
        num()
        {
            
        }
        num(int x,int y)
        {
            this.ff = x;
            this.ss =y;
       
        }
        public int getff()
        {
        return ff;
        }
        public int getss()
        {
        return ss;
        }
       public boolean equals(Object n1)
        {num n=(num)n1;
        if (this.ff==n.ff && this.ss==n.ss) return true;
        else return false;
            
            
        }
       public int compare(num n1,num n2)
        {  if (n1.ff!=n2.ff) return n1.ff-n2.ff;
            else return n1.ss-n2.ss;
            
            
        }    
        
    }

class FastReader
{
 
    public InputStream stream;
    private byte[] buf = new byte[1024];
    private int curChar;
    private int numChars;
    private SpaceCharFilter filter;
 
    public FastReader(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 char nc()
    {
        int c = read ();
        while (isSpaceChar (c))
            c = read ();
        return (char) c;
    }
    
    public int ni()
    {
        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')
            {
 
                
            }
            res *= 10;
            res += c - '0';
            c = read ();
        } while (!isSpaceChar (c));
        return res * sgn;
    }
 
    public long nl()
    {
        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;
    }
 
    public String ns()
    {
        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)
    {
        if (filter != null)
        {
            return filter.isSpaceChar (c);
        }
        return isWhitespace (c);
    }
 
    public static boolean isWhitespace(int c)
    {
        return c==' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
    }
 
    public String next()
    {
        return ns ();
    }
 
    public interface SpaceCharFilter
    {
        public boolean isSpaceChar(int ch);
    }
}