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.StringTokenizer;

public class C {

    final boolean ONLINE_JUDGE = System.getProperty("ONLINE_JUDGE") != null;
    BufferedReader in;
    PrintWriter out;
    StringTokenizer tok = new StringTokenizer("");

    void solve() throws IOException {
        int n = readInt();
        int t = readInt();
        char[] a = readString().toCharArray();
        char[] b = readString().toCharArray();

        char[] res = new char[n];

        int eq = 0;
        int dif = 0;
        for(int i = 0; i < n; i++) {
            if(a[i] == b[i]) eq++;
            else dif++;
        }
        int need1 = -1;
        int need2 = -1;
        int needB = -1;
        int needX = -1;
        for(int change = 0; change <= dif; change++) {
            int da = change;
            int x = t - da;
            if(x < 0 || x > eq) {
                continue;
            }

            int dbF = dif - change;
            int dbT = dif;
            int dbN = t - x;
            if(dbF <= dbN && dbN <= dbT) {
                need1 = da;
                need2 = dbN;
                needB = da + dbN - dif;
                needX = x;
            }
        }
        if(need1 < 0) {
            out.println(-1);
            return;
        }
        for(int i = 0; i < n; i++) {
            if(a[i] == b[i]) {
                if(needX != 0){
                    needX--;
                    res[i] = (a[i] == 'z' ? 'a' : (char)(a[i] + 1));
                } else {
                    res[i] = a[i];
                }
            } else {
                if(needB != 0) {
                    needB--;
                    need1--;
                    need2--;
                    for(int j = 0; j < 26; j++) {
                        if(j + 'a' != a[i] && j + 'a' != b[i]) {
                            res[i] = (char) (j + 'a');
                            break;
                        }
                    }
                } else if(need1 != 0) {
                    need1--;
                    res[i] = b[i];
                } else if(need2 != 0) {
                    need2--;
                    res[i] = a[i];
                }

            }
        }
        out.println(res);

    }


    void init() throws FileNotFoundException {
        if (ONLINE_JUDGE) {
            in = new BufferedReader(new InputStreamReader(System.in));
            out = new PrintWriter(System.out);
        } else {
            in = new BufferedReader(new FileReader("input.txt"));
            out = new PrintWriter("output.txt");
        }
    }

    String readString() throws IOException {
        while (!tok.hasMoreTokens()) {
            tok = new StringTokenizer(in.readLine());
        }
        return tok.nextToken();
    }

    int readInt() throws IOException {
        return Integer.parseInt(readString());
    }

    long readLong() throws IOException {
        return Long.parseLong(readString());
    }

    double readDouble() throws IOException {
        return Double.parseDouble(readString());
    }

    int[] readArr(int n) throws IOException {
        int[] res = new int[n];
        for (int i = 0; i < n; i++) {
            res[i] = readInt();
        }
        return res;
    }

    long[] readArrL(int n) throws IOException {
        long[] res = new long[n];
        for (int i = 0; i < n; i++) {
            res[i] = readLong();
        }
        return res;
    }

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

    public void run() {
        try {
            long t1 = System.currentTimeMillis();
            init();
            solve();
            out.close();
            long t2 = System.currentTimeMillis();
            System.err.println("Time = " + (t2 - t1));
        } catch (Exception e) {
            e.printStackTrace(System.err);
            System.exit(-1);
        }
    }
}