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 n, t;
string a, b;
int same;
int diff;
vector<int> s, d;
bool ss[100005];
bool d1[100005];
bool d2[100005];
int main() {
  cin >> n >> t;
  cin >> a >> b;
  t = n - t;
  for (int x = 0; x < n; x++) {
    if (a[x] == b[x])
      same++, s.push_back(x);
    else
      diff++, d.push_back(x);
  }
  if (t > diff / 2 + same) {
    printf("-1");
    return 0;
  }
  if (t < same) {
    diff = 0;
    same = t;
  } else {
    diff = (t - same);
  }
  for (int x = 0; x < same; x++) {
    ss[s[x]] = true;
  }
  for (int x = 0; x < diff; x++) {
    d1[d[x]] = true;
  }
  for (int x = diff; x < diff * 2; x++) {
    d2[d[x]] = true;
  }
  for (int x = 0; x < n; x++) {
    if (ss[x]) {
      printf("%c", a[x]);
    } else if (d1[x]) {
      printf("%c", a[x]);
    } else if (d2[x]) {
      printf("%c", b[x]);
    } else {
      for (int y = 'a';; y++) {
        if (y != a[x] && y != b[x]) {
          printf("%c", y);
          break;
        }
      }
    }
  }
}