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;
const int inf = 1e9 + 5, dy[] = {0, 0, 1, -1}, dx[] = {1, -1, 0, 0};
const long long linf = 5e18 + 5;
string s1, s2, s3;
int n, k, i, j, t, cnt, mndiff, diff, curr, eqmiss, as, bs;
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  ;
  cin >> n >> t;
  cin >> s1 >> s2;
  for (i = 0; i < n; ++i) {
    if (s1[i] == s2[i]) cnt++;
  }
  diff = n - cnt;
  mndiff = ((n - cnt) + 1) / 2;
  if (mndiff > t) {
    cout << "-1\n";
  } else {
    if (t > diff) {
      eqmiss = t - diff;
      for (i = 0; i < n; ++i) {
        if (s1[i] == s2[i] && eqmiss == 0) {
          s3.push_back(s1[i]);
        } else {
          char ch;
          for (char c : "abc")
            if (s1[i] != c && s2[i] != c) {
              ch = c;
              break;
            }
          s3.push_back(ch);
          if (s1[i] == s2[i]) eqmiss--;
        }
      }
    } else {
      as = bs = diff - t;
      for (i = 0; i < n; ++i) {
        if (s1[i] == s2[i]) {
          s3.push_back(s1[i]);
        } else if (s1[i] != s2[i] && (as || bs)) {
          if (as == bs) {
            s3.push_back(s1[i]);
            as--;
          } else {
            s3.push_back(s2[i]);
            bs--;
          }
        } else {
          char ch;
          for (char c : "abc")
            if (s1[i] != c && s2[i] != c) {
              ch = c;
              break;
            }
          s3.push_back(ch);
          if (s1[i] == s2[i]) eqmiss--;
        }
      }
    }
    cout << s3 << '\n';
  }
}