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.Scanner;

public class Main {


    static char diff(char a, char b) {
        char c = (char) Math.min(a, b);
        if (c > 'a')
            return 'a';
        c++;
        if (c == Math.max(a, b)) {
            c++;
        }
        return c;
    }


    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int t = sc.nextInt();
        char[] a = sc.next().toCharArray();
        char[] b = sc.next().toCharArray();
        char[] c = new char[n];
        int cnt = 0;
        int temp[] = new int[100010];
        for (int i = 0; i < n; i++) {
            if (a[i] != b[i]) {
                temp[cnt] = i;
                cnt++;
            }
        }

        if (cnt > 0 && t == 0) {
            System.out.println(-1);
            return;
        }

        if (cnt > t) {
            int r = cnt - t;
            int aa = 0, bb = 0;
            int id = 0;
            for (int i = 0; i < n; i++) {
                if (id < cnt) {
                    if (temp[id] == i) {
                        if (aa < r) {
                            c[i] = a[i];
                            aa++;
                        } else if (bb < r) {
                            c[i] = b[i];
                            bb++;
                        } else {
                            c[i] = diff(a[i], b[i]);
                        }
                        id++;
                        continue;
                    }
                }
                c[i] = a[i];
            }
            if (aa < r || bb < r) {
                System.out.println(-1);
            } else
                System.out.println(String.valueOf(c));
            return;
        }


        int r = t - cnt;
        int id = 0;
        int nnn = 0;
        for (int i = 0; i < n; i++) {
            if (id < cnt) {
                if (temp[id] == i) {
                    c[i] = diff(a[i], b[i]);
                    id++;
                    continue;
                }
            }
            if (nnn < r) {
                c[i] = diff(a[i], b[i]);
                nnn++;
                continue;
            }
            c[i] = a[i];
        }
        System.out.println(String.valueOf(c));
    }
}