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.io.*;

public class A {
    FastScanner in;
    PrintWriter out;

    public void solve() throws IOException {
        int n = in.nextInt();
        int t = n - in.nextInt();
        String s1 = in.next();
        String s2 = in.next();
        char[] ans = new char[n];
        for (int i = 0; i < n; i++) {
            ans[i] = '$';
        }
        int cnt1 = 0;
        int cnt2 = 0;
        int plus = 0;
        for (int i = 0; i < n; i++) {
            if (s1.charAt(i) == s2.charAt(i)) {
                plus++;
            }
        }
        if (cnt1 + plus >= t) {
            plus = t - cnt1;
            for (int j = 0; j < n; j++) {
                if (s1.charAt(j) == s2.charAt(j) && plus > 0) {
                    out.print(s1.charAt(j));
                    plus--;
                    continue;
                }
                if (ans[j] != '$') {
                    out.print(ans[j]);
                } else {
                    if (s1.charAt(j) != 'a' && s2.charAt(j) != 'a') {
                        out.print("a");
                    } else if (s1.charAt(j) != 'b' && s2.charAt(j) != 'b') {
                        out.print("b");
                    } else {
                        out.print("c");
                    }
                }
            }
            return;
        }
        for (int i = 0; i < n; i++) {
            if (s1.charAt(i) != s2.charAt(i)) {
                if (cnt1 < cnt2) {
                    ans[i] = s1.charAt(i);
                    cnt1++;
                } else if (cnt1 > cnt2) {
                    ans[i] = s2.charAt(i);
                    cnt2++;
                } else {
                    if (cnt1 + plus >= t) {
                        plus = t - cnt1;
                        for (int j = 0; j < n; j++) {
                            if (s1.charAt(j) == s2.charAt(j) && plus > 0) {
                                out.print(s1.charAt(j));
                                plus--;
                                continue;
                            }
                            if (ans[j] != '$') {
                                out.print(ans[j]);
                            } else {
                                if (s1.charAt(j) != 'a' && s2.charAt(j) != 'a') {
                                    out.print("a");
                                } else if (s1.charAt(j) != 'b' && s2.charAt(j) != 'b') {
                                    out.print("b");
                                } else {
                                    out.print("c");
                                }
                            }
                        }
                        return;
                    } else {
                        ans[i] = s1.charAt(i);
                        cnt1++;
                    }
                }
            }
        }
        if (cnt1 == cnt2 && cnt1 + plus >= t) {
            plus = t - cnt1;
            for (int j = 0; j < n; j++) {
                if (s1.charAt(j) == s2.charAt(j) && plus > 0) {
                    out.print(s1.charAt(j));
                    plus--;
                    continue;
                }
                if (ans[j] != '$') {
                    out.print(ans[j]);
                } else {
                    if (s1.charAt(j) != 'a' && s2.charAt(j) != 'a') {
                        out.print("a");
                    } else if (s1.charAt(j) != 'b' && s2.charAt(j) != 'b') {
                        out.print("b");
                    } else {
                        out.print("c");
                    }
                }
            }
            return;
        }
        out.println(-1);
    }

    public void run() {
        try {
            in = new FastScanner(System.in);
            out = new PrintWriter(System.out);
            solve();
            out.close();
        } catch (IOException e) {
            e.printStackTrace();
        }
    }

    class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        FastScanner(InputStream f) {
            br = new BufferedReader(new InputStreamReader(f));
        }

        String next() {
            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

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

    public static void main(String[] arg) {
        new A().run();
    }
}