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 CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int n, t, b[100020], cnt, p, q;
char s[100020], s1[100020], s2[100020];
char chose(char x, char y) {
  if (x != 'a' && y != 'a')
    return 'a';
  else if (x != 'b' && y != 'b')
    return 'b';
  else
    return 'c';
}
int main() {
  scanf("%d%d", &n, &t);
  scanf("%s", s1);
  scanf("%s", s2);
  cnt = 0;
  p = 0;
  q = 0;
  for (int i = 0; i < n; i++)
    if (s1[i] != s2[i]) cnt++;
  if (t < (cnt + 1) / 2) {
    printf("-1\n");
    return 0;
  }
  if (t <= cnt) {
    for (int i = 0; i < n; i++) {
      if (s1[i] == s2[i])
        s[i] = s1[i];
      else {
        p++;
        if (p <= 2 * t - cnt)
          s[i] = chose(s1[i], s2[i]);
        else if (p % 2 == 1)
          s[i] = s1[i];
        else
          s[i] = s2[i];
      }
    }
  } else {
    for (int i = 0; i < n; i++) {
      if (s1[i] == s2[i]) {
        q++;
        if (q <= t - cnt)
          s[i] = chose(s1[i], s1[i]);
        else
          s[i] = s1[i];
      } else {
        p++;
        s[i] = chose(s1[i], s2[i]);
      }
    }
  }
  printf("%s", s);
  return 0;
}