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 Main {

    private static Scanner sc = new Scanner(new BufferedReader(new InputStreamReader(System.in), 512000));
    static PrintWriter out = new PrintWriter(System.out);
    public static final char NULLCHAR = '\0';
    private static Random random = new Random(1);


    public static void solve() throws Exception {
        int n = in.nextInt();
        int tDifferent = in.nextInt();
        int match = n - tDifferent;

        int mapA[] = new int['z' + 1];
        int mapB[] = new int['z' + 1];

        String a = in.next();
        String b = in.next();

        char ans[] = new char[a.length()];
        int filled = 0;

        for (int i = 0; i < a.length(); i++) {
            if (a.charAt(i) == b.charAt(i) && match > 0) {
                ans[i] = a.charAt(i);
                match--;
                filled++;
                if (match < 1)
                    break;
            }
        }
        int aMatch = match;
        int bMatch = match;

        for (int i = 0; i < a.length(); i++) {
            if (ans[i] == NULLCHAR && aMatch > 0) {
                ans[i] = a.charAt(i);
                filled++;
                aMatch--;
                if (aMatch < 1)
                    break;
            }
        }

        for (int i = 0; i < b.length(); i++) {
            if (ans[i] == NULLCHAR && bMatch > 0) {
                ans[i] = b.charAt(i);
                filled++;
                bMatch--;
                if (bMatch < 1)
                    break;
            }
        }

        if (aMatch > 0 || bMatch > 0) {
            System.out.println(-1);
            return;
        }

        for (int i = 0; i < ans.length; i++) {
            if (ans[i] == NULLCHAR) {
                ans[i] = getDiffChar(a.charAt(i), b.charAt(i));
                filled++;
            }
        }
        if (filled != n) {
            System.out.println(-1);
        } else {
            System.out.println(new String(ans));
        }


    }

    public static char getDiffChar(final char a, final char b) {

        int diff;
        do {
            diff = random.nextInt(26) + 'a';
        }
        while (diff == a || diff == b);

        return (char) diff;
    }

    public static void test() {
    }

    public static void main(String args[]) throws Exception {
        in.init(System.in);
        solve();
        out.close();
    }


    public static class in {
        static BufferedReader reader;
        static StringTokenizer tokenizer;

        static void init(InputStream input) {
            reader = new BufferedReader(new InputStreamReader(input));
            tokenizer = new StringTokenizer("");
        }

        static String next() throws IOException {
            while (!tokenizer.hasMoreTokens())
                tokenizer = new StringTokenizer(reader.readLine());
            return tokenizer.nextToken();
        }

        static int nextInt() throws IOException {
            return Integer.parseInt(next());
        }

        static double nextDouble() throws IOException {
            return Double.parseDouble(next());
        }

        static long nextLong() throws IOException {
            return Long.parseLong(next());
        }
    }
}