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;
char s1[100005];
char s2[100005];
char s3[100005];
int diff[100005];
int main() {
  std::ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  int n, t;
  cin >> n >> t;
  cin >> s1;
  cin >> s2;
  int scount = 0;
  for (int i = 0; i < n; i++) {
    if (s1[i] != s2[i]) {
      diff[scount++] = i;
      s3[i] = 0;
    } else {
      s3[i] = s2[i];
    }
  }
  int d1 = scount, d2 = scount, turn = 0, c = 0;
  if (t < scount) {
    if (t < scount - scount / 2) {
      cout << -1;
      return 0;
    } else {
      c = 0;
      while (d1 != t || d2 != t) {
        if (turn % 2) {
          s3[diff[c]] = s1[diff[c]];
          d1--;
          turn = 0;
        } else {
          s3[diff[c]] = s2[diff[c]];
          d2--;
          turn = 1;
        }
        c++;
      }
      for (int j = 0; j < n; j++) {
        if (s3[j] == 0)
          for (int i = 'a'; i <= 'z'; i++) {
            if (i != s1[j] && i != s2[j]) {
              s3[j] = i;
              break;
            }
          }
      }
    }
  } else {
    c = 0;
    for (int i = 0; i < n; i++) {
      if (s3[i] == 0) {
        for (int j = 'a'; j <= 'z'; j++) {
          if (j != s1[i] && j != s2[i]) {
            s3[i] = j;
            c++;
            break;
          }
        }
      }
    }
    for (int i = 0; i < n; i++) {
      if (c == t) break;
      if (s2[i] == s1[i]) {
        for (int j = 'a'; j <= 'z'; j++) {
          if (j != s1[i] && j != s2[i]) {
            s3[i] = j;
            c++;
            break;
          }
        }
      }
    }
  }
  cout << s3;
  return 0;
}