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.IOException;
import java.io.InputStreamReader;
import java.util.Random;
import java.util.StringTokenizer;

public class MarinaAndVasya {
	
	public static void main(String[] args) {
		FastReader fs = new FastReader();
		int n = fs.nextInt(), t = fs.nextInt();
		String a = fs.nextLine(), b = fs.nextLine();
		
		char[] out = new char[n];
		int similar = (n - t) * 2;
		for(int i = 0; i < n && similar > 0; i++) {
			if(a.charAt(i) == b.charAt(i)) {
				out[i] = a.charAt(i);
				similar -= 2;
			}
		}
		
		boolean aTurn = true;
		for(int i = 0; i < n && similar > 0; i++) {
			if(a.charAt(i) !=  b.charAt(i)) {
				out[i] = aTurn? a.charAt(i) : b.charAt(i);
				aTurn = !aTurn;
				if(aTurn) {
					similar -= 2;
					t--;
				}
			}
		}
		
		for(int i = 0; i < n; i++) {
			if(out[i] == 0) {
				Random r = new Random();
				while(true) {
					char c = (char) (r.nextInt(26) + 97);
					if(c != a.charAt(i) && c != b.charAt(i)) {
						out[i] = c;
						t--;
						break;
					}
				}
			}
		}
		if(t > 0 || similar > 0)
			System.out.println(-1);
		else
			System.out.println(String.copyValueOf(out));
	}
		
	static class FastReader { 
        BufferedReader br; 
        StringTokenizer st; 
  
        public FastReader()  { 
            br = new BufferedReader(new
            		InputStreamReader(System.in)); 
        }
  
        String next() { 
            while (st == null || !st.hasMoreElements()) { 
                try { 
                    st = new StringTokenizer(br.readLine()); 
                } catch (IOException  e) { 
                    e.printStackTrace(); 
                } 
            } 
            return st.nextToken(); 
        } 
  
        int nextInt() { 
            return Integer.parseInt(next()); 
        } 
  
        long nextLong() { 
            return Long.parseLong(next()); 
        } 
  
        double nextDouble()  { 
            return Double.parseDouble(next()); 
        } 
  
        String nextLine()  { 
            String str = ""; 
            try { 
            	str = br.readLine(); 
        	} catch (IOException e) { 
        		e.printStackTrace(); 
        	} 
        	return str; 
        } 
	}
}