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:
/* Andy Rock
 * October 6, 2015
 *
 * C. Name - Link
 */

import java.io.*;
import java.util.*;

public class C
{
	public static void main(String[] args) throws IOException
	{
		BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st = new StringTokenizer(in.readLine());

		int n = Integer.parseInt(st.nextToken());
		int t = Integer.parseInt(st.nextToken());
		char[] s1 = in.readLine().toCharArray();
		char[] s2 = in.readLine().toCharArray();
		int ts = 0, fs = 0;
		boolean[] same = new boolean[n];
		for(int i=0;i<n;i++)
		{
			same[i] = s1[i] == s2[i];
			if(same[i])
				ts++;
			else
				fs++;
		}

		int f1 = -1, f2 = -1, t1 = -1;
		for(int i=0;i<=fs;i+=2)
			if(ts+i/2+fs-i >= t && i/2+fs-i <= t)
			{
				f1 = i;
				f2 = fs-f1;
				t1 = t-f2-f1/2;
			}

		boolean top = true;
		if(f1 == -1)
			System.out.println("-1");
		else
			for(int i=0;i<n;i++)
				if(same[i])
					if(t1 > 0)
					{
						System.out.print(s1[i] == 'a'?'b':'a');
						t1--;
					}
					else
						System.out.print(s1[i]);
				else
					if(f1 > 0)
					{
						if(top)
							System.out.print(s1[i]);
						else
							System.out.print(s2[i]);
						top = !top;
						f1--;
					}
					else
					{
						System.out.print((s1[i] == 'a' || s2[i] == 'a')?(s1[i] == 'b' || s2[i] == 'b')?'c':'b':'a');
					}
			
	}
}