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.util.*;

public class Problem3 {
	static int dist(String a, String b) {
		int d = 0;
		for (int i = 0; i < a.length(); ++i) {
			if (a.charAt(i) != b.charAt(i)) {
				++d;
			}
		}
		return d;
	}

	static char getDiffChar(char a, char b) {
		for (char c = 'a'; c <= 'z'; ++c) {
			if ((c != a) && (c != b)) {
				return c;
			}
		}
		return 'a';
	}

	public static void main(String[] args) {
		Scanner scanner = new Scanner(System.in);
		int n = scanner.nextInt();
		int t = scanner.nextInt();
		scanner.nextLine();
		String s1 = scanner.nextLine();
		String s2 = scanner.nextLine();
		char[] s3 = new char[n];
		int d = dist(s1, s2);
		if (d > 2 * t) {
			System.out.println(-1);
			return;
		} else {
			int third = t;
			if (d >= t) {
				third = 2 * t - d;
			}
			int first = t;
			int second = t;
			for (int i = 0; i < s1.length(); ++i) {
				if (s1.charAt(i) != s2.charAt(i)) {
					if (third > 0) {
						s3[i] = getDiffChar(s1.charAt(i), s2.charAt(i));
						--first;
						--second;
						--third;
					} else if (first > 0) {
						s3[i] = s2.charAt(i);
						--first;
					} else if (second > 0) {
						s3[i] = s1.charAt(i);
						--second;
					}
				} else {
					s3[i] = s1.charAt(i);
				}
			}
			for (int i = 0; (i < s1.length()) && (third > 0); ++i) {
				if (s1.charAt(i) == s2.charAt(i)) {
					s3[i] = getDiffChar(s1.charAt(i), s2.charAt(i));
					--third;
				}
			}
		}
		System.out.print(new String(s3));
	}
}