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 {
    public static Scanner in = new Scanner(
            new BufferedReader(new InputStreamReader(System.in)));
    public static PrintWriter out = new PrintWriter(
            new BufferedWriter(new OutputStreamWriter(System.out)));

    public static void main(String[] args) {
        int n = in.nextInt();
        int requiredDiff = in.nextInt();
        char[] s1 = in.next().toCharArray();
        char[] s2 = in.next().toCharArray();

        char[] s3 = new char[n];
        System.arraycopy(s1, 0, s3, 0, n);

        int diff = 0;
        for (int i = 0; i < n; i++)
            if (s1[i] != s2[i])
                diff++;

        int minDiff = (diff + 1) / 2;

        int requiredMerges = 0;
        int requiredChangeSim = 0;
        int requiredChangeDiff = 0;

        if (requiredDiff >= diff) {
            requiredMerges = 0;
            requiredChangeDiff = diff;
            requiredChangeSim = requiredDiff - diff;
        } else if (requiredDiff < diff) {
            requiredChangeSim = 0;
            requiredMerges = diff - requiredDiff;
            requiredChangeDiff = requiredDiff - requiredMerges;
        }

        if (requiredDiff < minDiff || requiredDiff > n) {
            out.println(-1);
        } else {
            boolean half = false;
            for (int i = 0; i < n; i++) {
                if (s1[i] != s2[i]) {
                    if (requiredMerges != 0) {
                        if (!half) {
                            s3[i] = s1[i];
                            half = true;
                        } else {
                            s3[i] = s2[i];
                            half = false;
                            requiredMerges--;
                        }
                    } else if (requiredMerges == 0 && requiredChangeDiff != 0) {
                        s3[i] = differentChar(s1[i], s2[i]);
                        requiredChangeDiff--;
                    }
                } else if (s1[i] == s2[i]) {
                    if (requiredChangeSim != 0) {
                        s3[i] = differentChar(s1[i], s2[i]);
                        requiredChangeSim--;
                    }
                }
            }
            out.println(s3);
        }

        out.close();
    }

    static char differentChar(char a, char b) {
        char c = ((a != 'z') ? (char) (a + 1) : 'a');
        if (b == c) {
            c = ((b != 'z') ? (char) (b + 1) : 'a');
        }
        return c;
    }

}