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.BufferedReader;
import java.io.ByteArrayOutputStream;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintStream;
import java.io.PrintWriter;
import java.io.StringReader;
import java.util.Arrays;

public class Main {
    int n;
    int t;

    public int f(char[] s1, char[] s2) {
        int d = 0;
        for (int i = 0; i < n; i++) {
            if (s1[i] != s2[i]) {
                d++;
            }
        }
        return d;
    }

    public void run() throws IOException {
        n = io.nextInt();
        t = io.nextInt();
        char[] s1 = io.next();
        char[] s2 = io.next();

        char[] xyz = {'x', 'y', 'z'};

        int t2 = f(s1, s2);

        int t1 = 0;
        if (t2 > t) {
            // d -> s
            for (int i = 0; i < n; i++) {
                if (t1 != t && s1[i] != s2[i]) {
                    if (t2 != t) {
                        s1[i] = s2[i];
                        t2--;
                        t1++;
                    }
                    else {
                        for (char c : xyz) {
                            if (c != s1[i] && c != s2[i]) {
                                s1[i] = c;
                                t1++;
                                break;
                            }
                        }
                    }
                }
            }
        }
        else if (t2 < t) {
            int t3 = t - t2;
            for (int i = 0; i < n; i++) {
                if (t3 > 0 && s1[i] == s2[i]) {
                    for (char c : xyz) {
                        if (c != s1[i]) {
                            s1[i] = c;
                            t3--;
                            t1++;
                            t2++;
                            break;
                        }
                    }
                }
                else if (s1[i] != s2[i]) {
                    for (char c : xyz) {
                        if (c != s1[i] && c != s2[i]) {
                            s1[i] = c;
                            t1++;
                            break;
                        }
                    }
                }
            }
        }
        else {
            for (int i = 0; i < n; i++) {
                if (t1 != t && s1[i] != s2[i]) {
                    for (char c : xyz) {
                        if (c != s1[i] && c != s2[i]) {
                            s1[i] = c;
                            t1++;
                            break;
                        }
                    }
                }
            }
        }
        if (t1 != t || t2 != t) {
            System.out.println(-1);
        }
        else {
            StringBuilder sb = new StringBuilder(n);
            for (int i = 0; i < n; i++) {
                sb.append(s1[i]);
            }
            System.out.println(sb);
        }
    }

    // @formatter:off
    private static final int mod = (int) 1e9 + 7;
    final IOFast io = new IOFast();

    void main() throws IOException { try { run(); } catch (RuntimeException ignore) { } finally { io.out.flush(); } }
    public static void main(String[] args) throws IOException { new Main().main(); }

    public static String dtos(double x, int n) {
        StringBuilder sb = new StringBuilder();
        if (x < 0) {
            sb.append('-');
            x = -x;
        }
        x += Math.pow(10, -n) / 2;
        sb.append((long) x);
        sb.append(".");
        x -= (long) x;
        for (int i = 0; i < n; i++) {
            x *= 10;
            sb.append((int) x);
            x -= (int) x;
        }
        return sb.toString();
    }

    public static class IOFast {
        private BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        private PrintWriter out = new PrintWriter(System.out);

        void setStringIn(String input) throws IOException { in.close(); in = new BufferedReader(new StringReader(input)); }
        void setStringOut(ByteArrayOutputStream output) throws IOException { System.out.flush(); System.setOut(new PrintStream(output)); }
        void setStringIO(String input, ByteArrayOutputStream output) throws IOException { setStringIn(input); setStringOut(output); }

        private static int pos, readLen;
        private static final char[] buffer = new char[1024 * 8];
        private static char[] str = new char[500*8*2];
        private static boolean[] isDigit = new boolean[256];
        private static boolean[] isSpace = new boolean[256];
        private static boolean[] isLineSep = new boolean[256];

        static { for(int i = 0; i < 10; i++) { isDigit['0' + i] = true; } isDigit['-'] = true; isSpace[' '] = isSpace['\r'] = isSpace['\n'] = isSpace['\t'] = true; isLineSep['\r'] = isLineSep['\n'] = true; }
        public int read() throws IOException { if(pos >= readLen) { pos = 0; readLen = in.read(buffer); if(readLen <= 0) { throw new RuntimeException(); } } return buffer[pos++]; }
        public int nextInt() throws IOException { int len = 0; str[len++] = nextChar(); len = reads(len, isSpace); int i = 0; int ret = 0; if(str[0] == '-') { i = 1; } for(; i < len; i++) ret = ret * 10 + str[i] - '0'; if(str[0] == '-') { ret = -ret; } return ret; }
        public long nextLong() throws IOException { int len = 0; str[len++] = nextChar(); len = reads(len, isSpace); int i = 0; long ret = 0; if(str[0] == '-') { i = 1; } for(; i < len; i++) ret = ret * 10 + str[i] - '0'; if(str[0] == '-') { ret = -ret; } return ret; }
        public char nextChar() throws IOException { while(true) { final int c = read(); if(!isSpace[c]) { return (char)c; } } }
        int reads(int len, boolean[] accept) throws IOException { try { while(true) { final int c = read(); if(accept[c]) { break; } if(str.length == len) { char[] rep = new char[str.length * 3 / 2]; System.arraycopy(str, 0, rep, 0, str.length); str = rep; } str[len++] = (char)c; } } catch(RuntimeException e) { ; } return len; }
        public char[] nextLine() throws IOException { int len = 0; str[len++] = nextChar(); len = reads(len, isLineSep); try { if(str[len-1] == '\r') { len--; read(); } } catch(RuntimeException e) { ; } return Arrays.copyOf(str, len); }
        public String nextString() throws IOException { return new String(next()); }
        public char[] next() throws IOException { int len = 0; str[len++] = nextChar(); len = reads(len, isSpace); return Arrays.copyOf(str, len); }
        public double nextDouble() throws IOException { return Double.parseDouble(nextString()); }
        public long[] nextLongArray(final int n) throws IOException { final long[] res = new long[n]; for(int i = 0; i < n; i++) { res[i] = nextLong(); } return res; }
        public int[] nextIntArray(final int n) throws IOException { final int[] res = new int[n]; for(int i = 0; i < n; i++) { res[i] = nextInt(); } return res; }
        public int[][] nextIntArray2D(final int n, final int k) throws IOException { final int[][] res = new int[n][]; for(int i = 0; i < n; i++) { res[i] = nextIntArray(k); } return res; }
        public int[][] nextIntArray2DWithIndex(final int n, final int k) throws IOException { final int[][] res = new int[n][k+1]; for(int i = 0; i < n; i++) { for(int j = 0; j < k; j++) { res[i][j] = nextInt(); } res[i][k] = i; } return res; }
        public double[] nextDoubleArray(final int n) throws IOException { final double[] res = new double[n]; for(int i = 0; i < n; i++) { res[i] = nextDouble(); } return res; }
    }
    // @formatter:on
}