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() {
  long long n, t, t1 = 0, t2 = 0, k = -1;
  string s1, s2, s3;
  cin >> n >> t >> s1 >> s2;
  s3.resize(n);
  for (int i = 0; i < n; i++) {
    if (s1[i] != s2[i]) {
      if (t2 >= t1) {
        t1++;
        s3[i] = s2[i];
      } else if (t1 >= t2) {
        t2++;
        s3[i] = s1[i];
      }
      k = i;
    } else if (s1[i] == s2[i]) {
      s3[i] = s1[i];
    }
  }
  if (t1 > t2) {
    if (s1[k] != 'a' && s2[k] != 'a') {
      s3[k] = 'a';
    } else if (s1[k] != 'b' && s2[k] != 'b') {
      s3[k] = 'b';
    } else if (s1[k] != 'c' && s2[k] != 'c') {
      s3[k] = 'c';
    }
    t2++;
  }
  if (t1 > t) {
    cout << -1 << endl;
  } else {
    for (int i = 0; i < n; i++) {
      if (s1[i] == s2[i] && t1 < t) {
        t1++;
        t2++;
        if (s1[i] == 'a') {
          s3[i] = 'b';
        } else {
          s3[i] = 'a';
        }
      }
    }
    for (int i = 0; i < n; i++) {
      if (s1[i] == s3[i] && t1 < t) {
        if (s1[i] != 'a' && s2[i] != 'a') {
          s3[i] = 'a';
        } else if (s1[i] != 'b' && s2[i] != 'b') {
          s3[i] = 'b';
        } else if (s1[i] != 'c' && s2[i] != 'c') {
          s3[i] = 'c';
        }
        t1++;
      } else if (s2[i] == s3[i] && t2 < t) {
        if (s1[i] != 'a' && s2[i] != 'a') {
          s3[i] = 'a';
        } else if (s1[i] != 'b' && s2[i] != 'b') {
          s3[i] = 'b';
        } else if (s1[i] != 'c' && s2[i] != 'c') {
          s3[i] = 'c';
        }
        t2++;
      }
    }
    cout << s3 << endl;
  }
  return 0;
}