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:
//swap(arr,i,j)
//HashMap sortByValue(map);
//long comb=nCr(5,2);
//int gcd(s,l);
//Pair p=new Pair(x,y);

import java.util.*;
import java.io.*;

public class Codeforces {

    InputStream is;
    PrintWriter out;
    String INPUT = "";

    //----------------------------------------------------------------------------------------------------//
    char addDifferent(char a,char b){
        char c=a;
        a=(char)Math.max(a,b);
        b=(char)Math.min(c,b);
        if((a-b)>1){
            c= (char)((a+b)/2);
        }
        else{
            if(a!='z') c=(char)(a+1);
            else c= 'a';
        }
        
        return c;
    }
    void solve() {
        int n=ni();
        int t=ni();
        char []a=ns(n);
        char []b=ns(n);
        int s=0;
        for (int i = 0; i < n; i++) {
            if(a[i]==b[i])s++;
        }
        char []c=new char[n];
        int l=(int)Math.ceil((n-s)/2.0);
        if(t<=n&&t>=l){
            int x=(n-t);
            if(t>=(n-s)){
                
                for (int i = 0; i < n; i++) {
                    if(x>0&&a[i]==b[i]){
                        c[i]=a[i];
                        x--;
                    }else{
                        c[i]=addDifferent(a[i], b[i]);
                    }
                }
            }
            else{
                x=x-s;
                int y=x;
                for (int i = 0; i < n; i++) {
                    if(a[i]==b[i]) c[i]=a[i];
                    else if(x>0||y>0){
                        if(x>0){
                            c[i]=a[i];
                            x--;
                        }
                        else if(y>0){
                            c[i]=b[i];
                            y--;
                        }
                        
                    }
                    else{
                        c[i]=addDifferent(a[i], b[i]);
                    }  
                }
            }
            String str=new String(c);
            out.println(str);
        }else{
            out.println(-1);
        }
    }

    //----------------------------------------------------------------------------------------------------//
    void swap(int a[], int l, int r) {
        int temp = a[l];
        a[l] = a[r];
        a[r] = temp;
    }

    long nCr(int n, int k) {
        long C[] = new long[k + 1];
        // nC0 is 1 
        C[0] = 1;
        for (int i = 1; i <= n; i++) {
            for (int j = Math.min(i, k); j > 0; j--) {
                C[j] = C[j] + C[j - 1];
            }
        }
        return C[k];
    }

    public int gcd(int s, int l) {
        if (s == 0) {
            return l;
        }

        return gcd(l % s, s);
    }

    public HashMap<Integer, Integer> sortByValue(HashMap<Integer, Integer> hm) {
        // Create a list from elements of HashMap 
        List<Map.Entry<Integer, Integer>> list
                = new LinkedList<>(hm.entrySet());

        //->change o1,o2 for reverseorder
        Collections.sort(list, (Map.Entry<Integer, Integer> o1, Map.Entry<Integer, Integer> o2) -> (o1.getValue()).compareTo(o2.getValue()));

        // put data from sorted list to hashmap  
        HashMap<Integer, Integer> temp = new LinkedHashMap<>();
        list.forEach((aa) -> {
            temp.put(aa.getKey(), aa.getValue());
        });
        return temp;
    }

    void run() throws Exception {
        is = System.in;//oj ? System.in : new ByteArrayInputStream(INPUT.getBytes());
        out = new PrintWriter(System.out);

        long s = System.currentTimeMillis();
        solve();
        out.flush();
        tr(System.currentTimeMillis() - s + "ms");
    }

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

    private byte[] inbuf = new byte[1024];
    public int lenbuf = 0, ptrbuf = 0;

    private int readByte() {
        if (lenbuf == -1) {
            throw new InputMismatchException();
        }
        if (ptrbuf >= lenbuf) {
            ptrbuf = 0;
            try {
                lenbuf = is.read(inbuf);
            } catch (IOException e) {
                throw new InputMismatchException();
            }
            if (lenbuf <= 0) {
                return -1;
            }
        }
        return inbuf[ptrbuf++];
    }

    private boolean isSpaceChar(int c) {
        return !(c >= 33 && c <= 126);
    }

    private int skip() {
        int b;
        while ((b = readByte()) != -1 && isSpaceChar(b));
        return b;
    }

    private double nd() {
        return Double.parseDouble(ns());
    }

    private char nc() {
        return (char) skip();
    }

    private String ns() {
        int b = skip();
        StringBuilder sb = new StringBuilder();
        while (!(isSpaceChar(b))) { // when nextLine, (isSpaceChar(b) && b != ' ')
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }

    private char[] ns(int n) {
        char[] buf = new char[n];
        int b = skip(), p = 0;
        while (p < n && !(isSpaceChar(b))) {
            buf[p++] = (char) b;
            b = readByte();
        }
        return n == p ? buf : Arrays.copyOf(buf, p);
    }

    private char[][] nm(int n, int m) {
        char[][] map = new char[n][];
        for (int i = 0; i < n; i++) {
            map[i] = ns(m);
        }
        return map;
    }

    private int[] na(int n) {
        int[] a = new int[n];
        for (int i = 0; i < n; i++) {
            a[i] = ni();
        }
        return a;
    }

    private int ni() {
        int num = 0, b;
        boolean minus = false;
        while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
        if (b == '-') {
            minus = true;
            b = readByte();
        }

        while (true) {
            if (b >= '0' && b <= '9') {
                num = num * 10 + (b - '0');
            } else {
                return minus ? -num : num;
            }
            b = readByte();
        }
    }

    private long nl() {
        long num = 0;
        int b;
        boolean minus = false;
        while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
        if (b == '-') {
            minus = true;
            b = readByte();
        }

        while (true) {
            if (b >= '0' && b <= '9') {
                num = num * 10 + (b - '0');
            } else {
                return minus ? -num : num;
            }
            b = readByte();
        }
    }

    private boolean oj = System.getProperty("ONLINE_JUDGE") != null;

    private void tr(Object... o) {
        if (!oj) {
            System.out.println(Arrays.deepToString(o));
        }
    }

    class Pair {

        /*SORTING PAIRS BY COMPARING Y OF PAIR.
    Pair[] p=new Pair[n];
    p[i]=new Pair(i,ni());
    Arrays.sort(p,( p1, p2) -> {return p1.y-p2.y;});
         */
        int x;
        int y;

        Pair(int u, int v) {
            x = u;
            y = v;
        }

        @Override
        public boolean equals(Object o) {
            if (this == o) {
                return true;
            }
            if (!(o instanceof Pair)) {
                return false;
            }
            Pair key = (Pair) o;
            return x == key.x && y == key.y;
        }

        @Override
        public int hashCode() {
            int result = x;
            result = 31 * result + y;
            return result;
        }

    }
}