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 final class marina_and_vasya
{
	static Scanner sc=new Scanner(System.in);
	static PrintWriter out=new PrintWriter(System.out);
	
	static void solve(char[] a,char[] b,int m,int n)
	{
		boolean[] s=new boolean[n];
		int c=0;
		int k=n-m;
		for(int i=0;i<n;i++)
		{
			if(a[i]==b[i] && k>0)
			{
				s[i]=true;
				c++;
				k--;
			}
		}
		int val1=(n-m)-c;
		if(n<(2*val1))
		{
			out.println("-1");
		}
		else
		{
			StringBuffer sb=new StringBuffer("");
			int m1=(n-m)-c;
			int m2=m1;
			for(int i=0;i<n;i++)
			{
				if(s[i])
				{
					sb.append(a[i]);
				}
				else
				{
					if(m1>0 && a[i]!=b[i])
					{
						sb.append(a[i]);
						m1--;
					}
					else if(m2>0 && a[i]!=b[i])
					{
						sb.append(b[i]);
						m2--;
					}
					else 
					{
						for(int j=97;j<=122;j++)
						{
							char c1=(char)j;
							if(c1!=a[i] && c1!=b[i])
							{
								sb.append(c1);
								break;
							}
						}
					}
				}
			}
			if(m1<=0 && m2<=0)
			{
				out.println(sb);
			}
			else
			{
				out.println("-1");
			}
		}
	}
	
	public static void main(String args[]) throws Exception
	{
		int n=sc.nextInt();
		int m=sc.nextInt();
		char[] a=sc.next().toCharArray();
		char[] b=sc.next().toCharArray();
		solve(a,b,m,n);
		out.close();
	}
}