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.*;

public class C
{

	FastScanner in;
	PrintWriter out;
	int i = 0, j = 0;


	void solve() {
		/**************START**************/
		int n = in.nextInt();
		int t = in.nextInt();
		char[] s1 = in.next().toCharArray();
		char[] s2 = in.next().toCharArray();
		char[] s3 = new char[n];
		int u = n - t;
		int topNeeded = 0;
		char[] diffChars = new char[n];
		int same = 0;
		boolean possible = true;
		int matched = 0;
		for (i = 0; i < s1.length; i++)
		{
			if (s1[i] == s2[i])
			{
				same++;
				if (s1[i] != 'a')
				{
					diffChars[i] = 'a';
				}
				else
				{
					diffChars[i] = 'b';
				}
			}
			else
			{
				if (s1[i] != 'a' && s2[i] != 'a')
				{
					diffChars[i] = 'a';
				}
				else if (s1[i] != 'b' && s2[i] != 'b')
				{
					diffChars[i] = 'b';
				}
				else
				{
					diffChars[i] = 'c';
				}
			}
		}
		if (u <= same)
		{
			topNeeded = 0;
		}
		else
		{
			topNeeded = (u - same);
			if (topNeeded * 2 > (n-same))
			{
				possible = false;
			}
		}
		int botNeeded = topNeeded;
		boolean done = false;
		if (u == 0)
		{
			done = true;
		}
		if (!possible)
		{
			out.println("-1");
		}
		else
		{
			for (i = 0; i < n; i++)
			{
				if (!done)
				{
					if (s1[i] == s2[i])
					{
						s3[i] = s1[i];
						matched++;
					}
					else
					{
						if (botNeeded > 0)
						{
							if (topNeeded == botNeeded)
							{
								s3[i] = s1[i];
								topNeeded--;
							}
							else
							{
								s3[i] = s2[i];
								botNeeded--;
								matched++;
								
							}
						}
						else
						{
							s3[i] = diffChars[i];
						}
					}
					if (matched == u)
					{
						done = true;
					}
				}
				else
				{
					s3[i] = diffChars[i];
				}
				
			}
			out.println(new String(s3));
		}





		/***************END***************/
	}

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

	void runIO() {
		in = new FastScanner(System.in);
		out = new PrintWriter(System.out);

		solve();

		out.close();
	}

	class FastScanner {
		BufferedReader br;
		StringTokenizer st;

		public FastScanner(File f) {
			try {
				br = new BufferedReader(new FileReader(f));
			} catch (FileNotFoundException e) {
				e.printStackTrace();
			}
		}

		public FastScanner(InputStream f) {
			br = new BufferedReader(new InputStreamReader(f));
		}

		String next() {
			while (st == null || !st.hasMoreTokens()) {
				String s = null;
				try {
					s = br.readLine();
				} catch (IOException e) {
					e.printStackTrace();
				}
				if (s == null)
					return null;
				st = new StringTokenizer(s);
			}
			return st.nextToken();
		}

		boolean hasMoreTokens() {
			while (st == null || !st.hasMoreTokens()) {
				String s = null;
				try {
					s = br.readLine();
				} catch (IOException e) {
					e.printStackTrace();
				}
				if (s == null)
					return false;
				st = new StringTokenizer(s);
			}
			return true;
		}

		int nextInt() {
			return Integer.parseInt(next());
		}

		long nextLong() {
			return Long.parseLong(next());
		}

		double nextDouble() {
			return Double.parseDouble(next());
		}
	}
}