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.*;
import java.math.*;

public class p584c {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        int n = in.nextInt();
        int t = in.nextInt();
        String s1 = in.next();
        String s2 = in.next();
        int m = s1.length();
        char[] s3 = new char[n];
        int d = 0;
        for (int i = 0; i < m; i++) {
            if (s1.charAt(i) != s2.charAt(i)) {
                d++;
            }
        }
        if (d > 2 * t) {
            out.println(-1);
            out.close();
            return;
        } else {
            int x1 = t, x2 = t, x3;
            if (d >= t) x3 = 2 * t - d;
            else x3 = t;
            for (int i = 0; i < s1.length(); i++) {
                if (s1.charAt(i) != s2.charAt(i)) {
                    if (x3 > 0) {
                        s3[i] = f(s1.charAt(i), s2.charAt(i));
                        --x1;
                        --x2;
                        --x3;
                    } else if (x1 > 0) {
                        s3[i] = s2.charAt(i);
                        --x1;
                    } else if (x2 > 0) {
                        s3[i] = s1.charAt(i);
                        --x2;
                    }
                } else {
                    s3[i] = s1.charAt(i);
                }
            }
            for (int i = 0; (i < s1.length()) && (x3 > 0); i++) {
                if (s1.charAt(i) == s2.charAt(i)) {
                    s3[i] = f(s1.charAt(i), s2.charAt(i));
                    --x3;
                }
            }
        }
        out.print(new String(s3));
        out.close();
    }

    public static char f(char a, char b) {
        for (char c = 'a'; c <= 'z'; c++) {
            if ((c != a) && (c != b)) {
                return c;
            }
        }
        return 'a';
    }

    static class Pair implements Comparable<Pair> {
        int x;
        int y;

        public Pair(int x, int y) {
            super();
            this.x = x;
            this.y = y;
        }

        @Override
        public int compareTo(Pair p) {
            return x < p.x ? -1 : x > p.x ? 1 : 0;
        }
    }

    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 String nextLine() {
            try {
                return reader.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return null;
        }

        public boolean hasMoreElements() {
            while (tokenizer == null || !tokenizer.hasMoreElements()) {
                String s;
                try {
                    s = reader.readLine();
                } catch (IOException e) {
                    return false;
                }
                tokenizer = new StringTokenizer(s);
            }
            return tokenizer.hasMoreElements();
        }
    }
}