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 C {

    MyScanner in;
    PrintWriter out;

    public static void main(String[] args) throws Exception {
        new C().run();
    }

    public void run() throws Exception {
        in = new MyScanner();
        out = new PrintWriter(System.out);

        solve();

        out.close();
    }

    char findThird(char c1, char c2) {
        if (c1 != 'a' && c2 != 'a') {
            return 'a';
        }
        if (c1 != 'b' && c2 != 'b') {
            return 'b';
        }
        return 'c';
    }

    public void solve() throws Exception {
        int n = in.nextInt();
        int t = in.nextInt();
        char[] s1 = in.next().toCharArray();
        char[] s2 = in.next().toCharArray();
        int d = 0;
        for (int i = 0; i < n; i++) {
            if (s1[i] != s2[i]) {
                d++;
            }
        }

        if (d > 2 * t) {
            out.println(-1);
            return;
        }
        char[] s = new char[n];
        if (d <= t) {
            int count = 0;
            for (int i = 0; i < n; i++) {
                if (s1[i] != s2[i]) {
                    s[i] = findThird(s1[i], s2[i]);
                    count++;
                } else {
                    s[i] = s1[i];
                }
            }
            int i = 0;
            while (i < n && count < t) {
                if (s1[i] == s2[i]) {
                    count++;
                    s[i] = findThird(s1[i], s2[i]);
                }
                i++;
            }
        } else {
            int count = 0;
            int changes = Math.min(d / 2 * 2, 2 * (n - t));
            boolean[] changed = new boolean[n];
            for (int i = 0; i < n; i++) {
                if (s1[i] == s2[i] || count == changes) {
                    s[i] = s1[i];
                } else {
                    count++;
                    changed[i] = true;
                    if (count % 2 == 0) {
                        s[i] = s1[i];
                    } else {
                        s[i] = s2[i];
                    }
                }
            }
            count /= 2;
            int i = 0;
            while (i < n && count < t) {
                if (!changed[i] && s1[i] != s2[i]) {
                    count++;
                    changed[i] = true;
                    s[i] = findThird(s1[i], s2[i]);
                }
                i++;
            }
            i = 0;
            while (i < n && count < t) {
                if (!changed[i]) {
                    count++;
                    s[i] = findThird(s1[i], s2[i]);
                }
                i++;
            }
        }
        out.println(String.valueOf(s));
    }

    class MyScanner {

        BufferedReader br;
        StringTokenizer st;

        public MyScanner() throws Exception {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String next() throws Exception {
            while ((st == null) || (!st.hasMoreTokens())) {
                String t = br.readLine();
                if (t == null) {
                    return null;
                }
                st = new StringTokenizer(t);
            }
            return st.nextToken();
        }

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

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

        boolean nextBoolean() throws Exception {
            return Boolean.parseBoolean(next());
        }

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