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:
//package codeforces.FiveEightFour;

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

public class TestC {

	/**
	 * @param args
	 */
	public static void main(String[] args) {
		new TestC().solve();
	}

	public void solve() {
		BufferedReader reader = new BufferedReader(new InputStreamReader(
				System.in));
		StringTokenizer ss;
		String s = "";
		try {
			while ((s = reader.readLine()) != null) {
				ss = new StringTokenizer(s);
				int n = Integer.valueOf(ss.nextToken()).intValue();
				int t = Integer.valueOf(ss.nextToken()).intValue();
				char[] a = reader.readLine().toCharArray();
				char[] b = reader.readLine().toCharArray();
				char[] c = new char[a.length];
				int same = 0;
				for (int i = 0; i < a.length; i++) {
					if (a[i] == b[i]) {
						same++;
					}
				}

				if ((n - t - same) * 2 > (n - same)) {
					System.out.println("-1");
				} else {
					int sameChange = t - n + same; // ��ͬ������Ҫ�ı��
					int sameA = n - same - t;//
					int sameB = sameA;
					int dif = t;
					if(sameA > 0) {
						dif = n - same - 2 * sameA;
					}
					int i = 0;
					while (i < n) {
						if (a[i] == b[i]) {
							c[i] = a[i];
							if (sameChange > 0) {
								c[i] = (c[i] == 'z' ? 'a' : (char) (c[i] + 1));
								sameChange--;
							}
							i++;
						} else {
							if (dif > 0) {
								char middle = 'a';
								while (a[i] == middle || b[i] == middle) {
									middle++;
								}
								c[i] = middle;
								dif --;
								i ++;
							} else if (sameA > 0) {
								c[i] = a[i];
								sameA--;
								i++;
							} else if (sameB > 0) {
								c[i] = b[i];
								sameB--;
								i++;
							} else {
								System.out.println("error");
							}
						}
					}
					System.out.println(c);
				}
			}
		} catch (NumberFormatException e) {
			e.printStackTrace();
		} catch (IOException e) {
			e.printStackTrace();
		}
	}

}