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;
long long MOD = 1000000007;
char ano(char x, char y) {
  for (char t = 'a'; t <= 'z'; t++) {
    if (t != x && t != y) return t;
  }
}
vector<int> c1, c2;
int main() {
  int n, t;
  cin >> n >> t;
  string s1, s2;
  cin >> s1 >> s2;
  int k1 = 0, k2 = 0;
  int d = 0, dd;
  for (int i = 0; i < n; i++)
    if (s1[i] != s2[i]) d++;
  dd = d;
  while (d + k1 > t) {
    if (d < 2) {
      cout << -1;
      return 0;
    }
    k1++;
    d -= 2;
  }
  k1 *= 2;
  k2 = t - d - k1;
  if (k2 > (n - dd)) {
    cout << -1;
    return 0;
  }
  string s = "";
  for (int i = 0; i < n; i++) {
    if (s1[i] == s2[i]) {
      if (k2 > 0) {
        s += ano(s1[i], s2[i]);
        k2--;
      } else
        s += s1[i];
      continue;
    } else {
      if (d > 0) {
        s += ano(s1[i], s2[i]);
        d--;
        continue;
      }
      if (k1 > 0) {
        if (k1 % 2 == 0)
          s += s1[i];
        else
          s += s2[i];
        k1--;
        continue;
      }
    }
  }
  cout << s;
}