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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.util.stream.IntStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.BufferedWriter;
import java.io.IOException;
import java.util.Random;
import java.io.InputStreamReader;
import java.util.StringTokenizer;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.io.BufferedReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Samin Arefin
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        TaskC solver = new TaskC();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskC {
        private Random random = new Random();

        private char genRand(char a, char b) {


            while (true) {
                char c = (char) (random.nextInt(26) + 'a');
                if (c != a && c != b) {
                    return c;
                }
            }

        }

        public void solve(int testNumber, InputReader in, OutputWriter out) {

            int n = in.nextInt();//1e5
            int t = in.nextInt();


            String s1 = in.nextLine();
            String s2 = in.nextLine();


            boolean[] matchInAll = new boolean[n];


            for (int i = 0; i < n; i++)
                if (s1.charAt(i) == s2.charAt(i))
                    matchInAll[i] = true;


            int[] notmatch = IntStream.range(0, n).filter(value -> !matchInAll[value]).toArray();
            int[] match = IntStream.range(0, n).filter(value -> matchInAll[value]).toArray();

            char[] ret = s1.toCharArray();

            if (notmatch.length == t) {
                for (int i : notmatch) {
                    ret[i] = genRand(s1.charAt(i), s2.charAt(i));
                }
                out.println(String.valueOf(ret));
                return;
            }

            if (notmatch.length < t) {
                for (int i : notmatch) {
                    ret[i] = genRand(s1.charAt(i), s2.charAt(i));
                }
                int rem = t - notmatch.length;
                for (int i : match) {
                    ret[i] = genRand(s1.charAt(i), s2.charAt(i));
                    if (--rem == 0) break;
                }
                out.println(String.valueOf(ret));
                return;
            }

            if ((n - t - match.length) * 2 > notmatch.length) {
                out.println(-1);
                return;
            }


            int todo = n - t;
            int up = match.length;
            int down = match.length;

            for (int i : notmatch) {

                if (up == todo && down == todo) ret[i] = genRand(s1.charAt(i), s2.charAt(i));

                else if (up == todo) {
                    ret[i] = s2.charAt(i);
                    down++;
                } else {
                    ret[i] = s1.charAt(i);
                    up++;
                }

            }

            out.println(String.valueOf(ret));
        }

    }

    static class InputReader extends BufferedReader {
        private StringTokenizer token;

        public InputReader(InputStream stream) {
            super(new InputStreamReader(stream));
        }

        public String next() {
            while (token == null || !token.hasMoreElements()) {
                try {
                    token = new StringTokenizer(readLine(), ", ");
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }

            return token.nextToken();
        }

        public String nextLine() {
            String string = "";
            try {
                string = readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return string;
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

    }

    static class OutputWriter extends PrintWriter {
        public OutputWriter(OutputStream outputStream) {
            super(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            super(writer);
        }

        public void close() {
            super.close();
        }

    }
}