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.util.*;

public class A1{
     
    public static void main(String args[]){
        Scanner in = new Scanner(System.in);
        int n = in.nextInt();
        int t = in.nextInt();
        String s1=  in.next();
        String s2 = in.next();
        char c1[] = s1.toCharArray();
        char c2[] = s2.toCharArray();
        int count=0;
        for(int i=0;i<n;i++){
            if(s1.charAt(i)!=s2.charAt(i))
                count++;
        }
        
        if(t>count)
        {
            int rem = t-count;
            for(int i=0;i<n;i++){
                if(s1.charAt(i)==s2.charAt(i) && rem>0){
                    if(c1[i]!='z')
                        System.out.print((char)(s1.charAt(i)+1));
                    else
                        System.out.print((char)(c1[i]-1));
                    rem--;
                }
                else if(c1[i]==c2[i])
                    System.out.print(c1[i]);
                else{
                    if(c1[i]!='z')
                        if(c1[i]+1!=c2[i])
                            System.out.print((char)(s1.charAt(i)+1));
                        else
                            if(c1[i]=='a')
                                System.out.print((char)(c1[i]+2));
                            else
                                System.out.print((char)(c1[i]-1));
                    else
                        if(c1[i]-1!=c2[i])
                            System.out.print((char)(s1.charAt(i)-1));
                        else
                            if(c1[i]=='z')
                                System.out.print((char)(c1[i]-2));
                            else
                                System.out.print((char)(c1[i]+1));
                }
            }
            return;
        }
        else if(t>=(count+1)/2){
            boolean flag = true;
            for(int i=0;i<n;i++){
                if(s1.charAt(i)!=s2.charAt(i)){
                    if(count<2*t){
                        if(c1[i]!='z')
                            if(c1[i]+1!=c2[i])
                                System.out.print((char)(s1.charAt(i)+1));
                            else
                                if(c1[i]=='a')
                                    System.out.print((char)(c1[i]+2));
                                else
                                    System.out.print((char)(c1[i]-1));
                        else
                            if(c1[i]-1!=c2[i])
                                System.out.print((char)(s1.charAt(i)-1));
                            else
                                if(c1[i]=='z')
                                    System.out.print((char)(c1[i]-2));
                                else
                                    System.out.print((char)(c1[i]+1));
                        count--;
                        t--;
                    }
                    else{
                        if(flag){
                            System.out.print(c1[i]);
                            flag = false;
                        }
                        else{
                            System.out.print(c2[i]);
                            flag = true;
                        }
                    }
                }
                else{
                    System.out.print(c1[i]);
                }
            }
        }
        else{
            System.out.println("-1");
        }
    }
}