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;
  string a, b;
  cin >> n >> t;
  cin >> a >> b;
  vector<char> c(n, '!');
  int sa = n - t;
  for (int i = 0; i < n; i++) {
    if (sa == 0) break;
    if (a[i] == b[i]) {
      c[i] = a[i];
      sa--;
    }
  }
  int as, bs;
  if (sa == 0) {
    for (int i = 0; i < n; ++i) {
      if (c[i] == '!') {
        if (a[i] != 'a' && b[i] != 'a') {
          c[i] = 'a';
        } else if (a[i] == 'a' && b[i] == 'a') {
          c[i] = 'b';
        } else {
          if (a[i] == 'a') {
            if (b[i] == 'b')
              c[i] = 'c';
            else
              c[i] = 'b';
          } else {
            if (a[i] == 'b')
              c[i] = 'c';
            else
              c[i] = 'b';
          }
        }
      }
    }
    as = bs = 0;
  } else {
    as = sa, bs = sa;
    for (int i = 0; i < n; ++i) {
      if (c[i] == '!') {
        if (as) {
          c[i] = a[i];
          as--;
        } else {
          if (bs) {
            c[i] = b[i];
            bs--;
          } else {
            if (a[i] != 'a' && b[i] != 'a') {
              c[i] = 'a';
            } else if (a[i] == 'a' && b[i] == 'a') {
              c[i] = 'b';
            } else {
              if (a[i] == 'a') {
                if (b[i] == 'b')
                  c[i] = 'c';
                else
                  c[i] = 'b';
              } else {
                if (a[i] == 'b')
                  c[i] = 'c';
                else
                  c[i] = 'b';
              }
            }
          }
        }
      }
    }
  }
  if (as > 0 || bs > 0)
    cout << -1;
  else
    for (int i = 0; i < n; ++i) {
      cout << c[i];
    }
}