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 notab(char a, char b) {
  for (char i = 'a'; i <= 'z'; i++) {
    if (i != b && i != a) return i;
  }
}
int main() {
  ios::sync_with_stdio(false);
  int n, t;
  cin >> n >> t;
  string A, B;
  cin >> A;
  cin >> B;
  int ct = 0;
  string C = A;
  for (int i = 0; i < A.length(); i++)
    if (A[i] != B[i]) ct++;
  if ((ct + 1) / 2 > t) {
    cout << -1;
    return 0;
  } else {
    if (t <= ct) {
      int x = 2 * (ct - t);
      int y = 2 * (ct - t);
      int start = A.length();
      for (int i = 0; i < A.length(); i++) {
        if (!x) {
          start = i;
          break;
        }
        if (A[i] != B[i]) {
          if (x > y / 2)
            C[i] = A[i];
          else
            C[i] = B[i];
          x--;
        }
      }
      for (int i = start; i < A.length(); i++) {
        if (A[i] != B[i]) C[i] = notab(A[i], B[i]);
      }
      for (int i = 0; i < A.length(); i++) {
        if (A[i] == B[i]) C[i] = A[i];
      }
    } else {
      for (int i = 0; i < A.length(); i++) {
        if (A[i] != B[i]) {
          C[i] = notab(A[i], B[i]);
        }
      }
      int rt = t - ct, start = A.length();
      for (int i = 0; i < A.length(); i++) {
        if (!rt) {
          start = i;
          break;
        }
        if (A[i] == B[i]) {
          C[i] = notab(A[i], B[i]);
          rt--;
        }
      }
      for (int i = start; i < A.length(); i++)
        if (A[i] == B[i]) C[i] = A[i];
    }
    cout << C << "\n";
  }
}