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.*;
import java.io.*;
import java.math.*;
public final class Solution 
{
    public static void main(String[] args)
    {
    	 Reader input = new Reader();
         PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));
         int n = input.nextInt() , t = input.nextInt();
         int d = n - t;
         char[] a = input.next().toCharArray();
         char[] b = input.next().toCharArray();
         char[] result = new char[n];
         Arrays.fill(result, '0');
         for(int i = 0 ; i < n ; i++)
         {
        	 if(a[i] == b[i])
        	 {
        		 result[i] = a[i];
        		 d--;
        		 if(d < 0)
        		 {
        			 result[i] = a[i] == 'a'? 'b' : 'a';
        			 d = 0;
        		 }        			 
        	 }
         }
         int d1 = d , d2 = d;
         for(int i = 0 ; i < n ; i++)
         {
        	 if(result[i] != '0')
        		 continue;
        	 if(d1 != 0)
        	 {
        		 result[i] = a[i];
        		 d1--;
        	 }
        	 else if(d2 != 0)
        	 {
        		 result[i] = b[i];
        		 d2--;
        	 }
        	 else
        	 {
        		 for(char s = 'a' ; s <= 'c' ; s++)
        		 {
        			 if(s != a[i] && s != b[i])
        			 {
        				 result[i] = s;
        				 break;
        			 }
        		 }
        	 }
         }
         if(d1 != 0 || d2 != 0)
        	 out.println(-1);
         else
         {
             for(int i = 0 ; i < n ; i++)
            	 out.print(result[i]);
         }
		 out.close();	 
    } 
    public static class Reader
    {
    	BufferedReader br;
    	StringTokenizer st;
    	public Reader()
    	{
    		br = new BufferedReader(new InputStreamReader(System.in));    		
    	}
    	public String next()
    	{
    		try
    		{
        		if(st == null || !st.hasMoreTokens())
        			st = new StringTokenizer(br.readLine());
    		}
    		catch(IOException ex)
    		{
    			ex.printStackTrace();
    			System.exit(1);
    		}    		
    		return st.nextToken();
    	}
    	public int nextInt()
    	{
    		return Integer.parseInt(next());
    	}
    	public double nextDouble()
    	{
    		return Double.parseDouble(next());
    	}
    	public long nextLong()
    	{
    		return Long.parseLong(next());
    	}
    	public String nextLine()
    	{
    		try
    		{
    			return br.readLine();
    		}
    		catch(IOException ex)
    		{
    			ex.printStackTrace();
    			System.exit(1);
    		}
    		return "";
    	}
    }
}