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 b[100001];
int main(int argc, char const *argv[]) {
  int n, t;
  cin >> n >> t;
  string s1, s2;
  cin >> s1 >> s2;
  int same = 0, diff = 0;
  for (int i = 0; i < n; i++) {
    if (s1[i] != s2[i])
      diff++;
    else
      same++;
    b[i] = -11;
  }
  if (t == 0 && diff == 1) {
    cout << "-1";
    return 0;
  }
  if (diff <= t) {
    int c = 0;
    for (int i = 0; i < n; i++) {
      if (s1[i] != s2[i]) {
        b[i] = -1;
        c++;
      }
    }
    for (int i = 0; i < n; i++) {
      if (c < t) {
        if (s1[i] == s2[i]) {
          b[i] = -1;
          c++;
        }
      } else
        break;
    }
    if (c == t) {
      for (int i = 0; i < n; i++) {
        if (b[i] == -1) {
          for (char j = 'a'; j <= 'z'; j++) {
            if (j != s1[i] && j != s2[i]) {
              cout << j;
              break;
            }
          }
        } else
          cout << s1[i];
      }
    } else
      cout << "-1";
  } else if (diff > t) {
    int t1 = t, t2 = t;
    int c1 = 0, c2 = 0, c3 = 0;
    for (int i = 0; i < n; i++) {
      if (diff > t1) {
        if (s1[i] != s2[i] && c3 % 2 == 0) {
          b[i] = 1;
          t1 -= 1;
          diff--;
          c1++;
          c3++;
        } else if (s1[i] != s2[i] && c3 % 2 != 0) {
          b[i] = 0;
          t2 -= 1;
          diff--;
          c2++;
          c3++;
        }
      } else {
        if (s1[i] != s2[i]) {
          b[i] = -1;
          diff--;
          t1--;
          c1++;
          c2++;
        }
      }
    }
    if (c1 == t && c2 == t) {
      for (int i = 0; i < n; i++) {
        if (b[i] == -1) {
          for (char j = 'a'; j <= 'z'; j++) {
            if (j != s1[i] && j != s2[i]) {
              cout << j;
              break;
            }
          }
        } else if (b[i] == 1) {
          cout << s1[i];
        } else
          cout << s2[i];
      }
    } else
      cout << "-1";
  }
  return 0;
}