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.BufferedReader;
import java.io.BufferedWriter;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
 
public class Main
{
    public char get(char a,char b)
    {
        for(char i='a';i<='z';i++)
            if(i!=a&&i!=b) return i;
        return '0';
    }
    public Main() throws Exception
    {
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        BufferedWriter out = new BufferedWriter(new OutputStreamWriter(System.out));
        String str[]=in.readLine().split(" ");
        int n=Integer.parseInt(str[0]);
        int t=Integer.parseInt(str[1]);
        String a=in.readLine();
        String b=in.readLine();
        int count=0;
        for(int i=0;i<n;i++)
            if(a.charAt(i)==b.charAt(i)) count++;
        if(t==0&&!a.equals(b))
        {
            out.write("-1\n");
        }
        else if(count<n-t)
        {
            int diff=n-t-count;
            int left=n-count;
            if(2*diff<=left)
            {
                int v=0;
                char ans[]=new char[n];
                boolean is=false;
                for(int i=0;i<n;i++)
                {
                    if(a.charAt(i)==b.charAt(i)) ans[i]=a.charAt(i);
                    else if(v<diff)
                    {
                        if(!is)
                        {
                            ans[i]=a.charAt(i);
                            is=true;
                        }
                        else
                        {
                            ans[i]=b.charAt(i);
                            is=false;
                            v++;
                        }
                    }
                    else ans[i]=get(a.charAt(i),b.charAt(i));
                }
                out.write(new String(ans)+"\n");
            }
            else out.write("-1\n");
        }
        else if(count==n-t)
        {
            char ans[]=new char[n];
            for(int i=0;i<n;i++)
            {
                if(a.charAt(i)==b.charAt(i)) ans[i]=a.charAt(i);
                else ans[i]=get(a.charAt(i),b.charAt(i));
            }
            out.write(new String(ans)+"\n");
        }
        else if(count>n-t)
        {
            int val=0;
            char ans[]=new char[n];
            for(int i=0;i<n;i++)
            {
                if(a.charAt(i)==b.charAt(i)&&val<n-t)
                {
                    ans[i]=a.charAt(i);
                    val++;
                }
                else ans[i]=get(a.charAt(i),b.charAt(i));
            }
            out.write(new String(ans)+"\n");
        }
        out.flush();
    }
    public static void main(String args[]) throws Exception
    {
        new Main();
    }
}