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;
const int MAXN = 100 * 1000 + 1;
char s1[MAXN], s2[MAXN];
char diff(char q, char w) {
  for (char a = 'a'; a <= 'z'; ++a) {
    if (a != w && a != q) return a;
  }
  return 'X';
}
int main() {
  int n, t;
  cin >> n >> t;
  cin >> s1 >> s2;
  int x = 0, y = 0;
  for (int a = 0; a < n; ++a) {
    if (s1[a] == s2[a])
      ++x;
    else
      ++y;
  }
  1;
  ;
  1;
  ;
  int maxi = -1;
  for (int i = 0; i <= y; ++i) {
    if ((y - i) & 1) continue;
    if (i + (y - i) / 2 <= t) {
      maxi = i;
    }
  }
  if (maxi == -1) {
    cout << -1;
    return 0;
  }
  1;
  ;
  if (maxi + (y - maxi) / 2 + x < t) {
    cout << -1;
    return 0;
  }
  int chx = t - (maxi + (y - maxi) / 2);
  1;
  ;
  bool b = 0;
  for (int a = 0; a < n; ++a) {
    if (s1[a] == s2[a]) {
      if (chx > 0) {
        cout << diff(s1[a], s1[a]);
        --chx;
      } else
        cout << s1[a];
    } else {
      if (maxi > 0) {
        cout << diff(s1[a], s2[a]);
        --maxi;
      } else {
        if (b)
          cout << s1[a];
        else
          cout << s2[a];
        b = !b;
      }
    }
  }
  return 0;
}