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 main() {
  int n, t;
  cin >> n >> t;
  string s1, s2;
  vector<char> s3(n);
  cin >> s1 >> s2;
  int k = n - t, q = 0;
  for (int i = 0; i < n; i++) {
    if (s1[i] == s2[i]) {
      q++;
    }
  }
  if (k <= q) {
    for (int i = 0; i < n; i++) {
      if (s1[i] == s2[i] && k > 0) {
        s3[i] = s1[i];
        k--;
      } else {
        if (s1[i] > s2[i]) {
          if (s1[i] == 'z') {
            if (s2[i] == 'a') {
              s3[i] = s2[i] + 1;
            } else {
              s3[i] = s2[i] - 1;
            }
          } else {
            s3[i] = s1[i] + 1;
          }
        } else {
          if (s2[i] == 'z') {
            if (s1[i] == 'a') {
              s3[i] = s1[i] + 1;
            } else {
              s3[i] = s1[i] - 1;
            }
          } else {
            s3[i] = s2[i] + 1;
          }
        }
      }
    }
  } else {
    if (n - q < 2 * (k - q)) {
      cout << "-1";
      return 0;
    } else {
      for (int i = 0; i < n; i++) {
        if (s1[i] == s2[i]) {
          s3[i] = s1[i];
        }
      }
      int t1 = 0, t2 = 0;
      for (int i = 0; i < n; i++) {
        if (s3[i] != s1[i] && t1 < k - q) {
          s3[i] = s1[i];
          t1++;
        } else if (s3[i] != s2[i] && t2 < k - q) {
          s3[i] = s2[i];
          t2++;
        } else if (s3[i] != s2[i] && s3[i] != s1[i]) {
          if (s1[i] > s2[i]) {
            if (s1[i] == 'z') {
              if (s2[i] == 'a') {
                s3[i] = s2[i] + 1;
              } else {
                s3[i] = s2[i] - 1;
              }
            } else {
              s3[i] = s1[i] + 1;
            }
          } else if (s1[i] < s2[i]) {
            if (s2[i] == 'z') {
              if (s1[i] == 'a') {
                s3[i] = s1[i] + 1;
              } else {
                s3[i] = s1[i] - 1;
              }
            } else {
              s3[i] = s2[i] + 1;
            }
          } else {
            if (s2[i] == 'z') {
              s3[i] = s2[i] - 1;
            } else {
              s3[i] = s2[i] + 1;
            }
          }
        }
      }
    }
  }
  for (int i = 0; i < n; i++) {
    cout << s3[i];
  }
  return 0;
}