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.Scanner;
public class Main {
	public static char random(char x,char y){
		int x1,y1,z1;
		char z;
		x1=Math.min((int)x,(int)y);
		y1=Math.max((int)x,(int)y);
		if(x1==97){
			if(y1==122){
				z1=x1+1;
				z=(char)z1;
				return z;			
			}
			else{
			z1=y1+1;
			z=(char)z1;
			return z;
			}
		}
		else{
		z1=x1-1;
		z=(char)z1;
		return z;
		}
	}
	public static char random1(char x){
		int x1;
		x1=(int)x;
		if(x1==97)
			x1=x1+1;
		else
			x1=x1-1;
			x=(char)x1;
		return x;	
	}
	
	public static void main(String[] args) {
		Scanner scan=new Scanner(System.in);
		int n,t,i,k=0,k1=1,k2=1;
		char b1,b2,c;
		n=scan.nextInt();
		t=scan.nextInt();
		String a1,a2,a3;
		a3=scan.nextLine();
		a1=scan.nextLine();
		a2=scan.nextLine();
		for(i=1;i<=n;i++){
			b1=a1.charAt(i-1);
			b2=a2.charAt(i-1);
			if(b1!=b2)
				k++;		
		}
		if(k>2*t)
			System.out.println("-1");
		if(k<=2*t&&k>t){
			for(i=1;i<=n;i++){
				b1=a1.charAt(i-1);
				b2=a2.charAt(i-1);
				if(b1!=b2){
					if(k1<=k-t){
						c=b1;
						System.out.print(c);
					}
					if(k1>k-t&&k1<=2*(k-t)){
						c=b2;
						System.out.print(c);					
					}
					if(k1>2*(k-t)){
						c=random(b1,b2);
						System.out.print(c);
					}
					k1++;					
				}
				else{
					c=b1;
					System.out.print(c);
				}				
			}		
		}
		if(k<=t){
			for(i=1;i<=n;i++){
				b1=a1.charAt(i-1);
				b2=a2.charAt(i-1);
				if(b1!=b2){
					c=random(b1,b2);
					System.out.print(c);		
				}
				else{	
					if(k2<=t-k){
						c=random1(b1);
						System.out.print(c);						
					}
					else{
						c=b1;
						System.out.print(c);						
					}
					k2++;
				}
			}
		}		
	}	
}