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.lang.*;
import java.io.*;
import java.math.*;
import java.util.concurrent.*;

public class Main {
    //---------------------------------------------------------------------------

    static boolean isPrime(int n) {
        if (n < 2) {
            return false;
        }
        if (n == 2) {
            return true;
        }
        if (n % 2 == 0) {
            return false;
        }
        for (int i = 3; i * i <= n; i++) {
            if (n % i == 0) {
                return false;
            }
        }
        return true;
    }

    public static void main(String[] args) {
        InputReader in = new InputReader(System.in);
        PrintWriter out = new PrintWriter(System.out);
        //-----------------------------------------------------------------------
        int n = in.nextInt();
        int t = in.nextInt();
        int k = n - t;
        char[] a = in.nextCharArray();
        char[] b = in.nextCharArray();
        int cd = 0;
        for (int i = 0; i < n; i++) {
            if (a[i] != b[i]) {
                cd++;
            }
        }
        int cs = n - cd;
        char[] c = new char[n];
        Arrays.fill(c, '?');
        int ka = k;
        int kb = k;
        if (k <= cs) {
            ka = 0;
            kb = 0;
            for (int i = 0; i < n; i++) {
                if (k == 0) {
                    break;
                }
                if (a[i] == b[i]) {
                    c[i] = a[i];
                    k--;
                }
            }
            for (int i = 0; i < n; i++) {
                if (c[i] == '?') {
                    for (char j = 'a'; j <= 'z'; j++) {
                        if (a[i] != j && b[i] != j) {
                            c[i] = j;
                            break;
                        }
                    }
                }
            }
        } else {
            for (int i = 0; i < n; i++) {
                if (a[i] == b[i]) {
                    c[i] = a[i];
                    ka--;
                    kb--;
                }
            }
            for (int i = 0; i < n; i++) {
                if (c[i] == '?') {
                    if (ka > 0) {
                        c[i] = a[i];
                        ka--;
                    } else if (kb > 0) {
                        c[i] = b[i];
                        kb--;
                    } else {
                        for (char j = 'a'; j <= 'z'; j++) {
                            if (a[i] != j && b[i] != j) {
                                c[i] = j;
                                break;
                            }
                        }
                    }
                }
            }
        }
        if (ka > 0 || kb > 0) {
            out.println(-1);
        } else {
            for (int i = 0; i < n; i++) {
                out.print(c[i]);
            }
            out.println();
        }
        //-----------------------------------------------------------------------
        out.close();
    }

    //---------------------------------------------------------------------------
    static void shuffleArray(int[] ar) {
        Random rnd = ThreadLocalRandom.current();
        for (int i = ar.length - 1; i > 0; i--) {
            int index = rnd.nextInt(i + 1);
            int a = ar[index];
            ar[index] = ar[i];
            ar[i] = a;
        }
    }

    static class Pair implements Comparator {

        int first;
        long second;

        public Pair() {

        }

        public Pair(int f, long s) {
            this.first = f;
            this.second = s;
        }

        @Override
        public int compare(Object o1, Object o2) {
            Pair p1 = (Pair) o1;
            Pair p2 = (Pair) o2;
            int ret = Integer.compare(p1.first, p2.first);
            if (ret == 0) {
                ret = Long.compare(p1.second, p2.second);
            }
            return ret;
        }
    }

    static class InputReader {

        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

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

        public long nextLong() {
            return Long.parseLong(next());
        }

        public double nextDouble() {
            return Double.parseDouble(next());
        }

        public char[] nextCharArray() {
            return next().toCharArray();
        }

        public boolean hasNext() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    String s = reader.readLine();
                    if (s == null) {
                        return false;
                    }
                    tokenizer = new StringTokenizer(s);
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return true;
        }

        public void skipLine() {
            try {
                tokenizer = null;
                reader.readLine();
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
    }
}