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 len, d;
int f(string s1, string s2) {
  int cnt = 0;
  for (int i = 0; i < len; i++)
    if (s1[i] != s2[i]) cnt++;
  return cnt;
}
char totallyDifferentChar(char c1, char c2) {
  for (char i = 'a'; i <= 'z'; i++)
    if (c1 != i && c2 != i) return i;
}
int main() {
  scanf("%d %d", &len, &d);
  string s1, s2;
  cin >> s1 >> s2;
  int fval = f(s1, s2);
  if (fval <= d) {
    string ans = s1;
    int goalCnt = d;
    for (int i = 0; i < len && goalCnt; i++)
      if (s1[i] != s2[i]) {
        ans[i] = totallyDifferentChar(s1[i], s2[i]);
        goalCnt--;
      }
    goalCnt = d - fval;
    for (int i = 0; i < len && goalCnt; i++)
      if (s1[i] == s2[i]) {
        ans[i] = totallyDifferentChar(s1[i], s2[i]);
        goalCnt--;
      }
    cout << ans << endl;
  } else {
    string ans = s1;
    int same_N = fval - d;
    if (same_N * 2 <= fval) {
      for (int i = 0; i < len; i++)
        if (s1[i] != s2[i]) ans[i] = totallyDifferentChar(s1[i], s2[i]);
      int goalCnt = same_N;
      for (int i = 0; i < len && goalCnt; i++)
        if (s1[i] != s2[i]) {
          ans[i] = s1[i];
          goalCnt--;
        }
      goalCnt = same_N;
      for (int i = len - 1; i >= 0 && goalCnt; i--)
        if (s1[i] != s2[i]) {
          ans[i] = s2[i];
          goalCnt--;
        }
      cout << ans << endl;
    } else
      printf("-1\n");
  }
  return 0;
}