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;
char s[100005], a[100005], b[100005];
bool f[100005];
int n, m;
int main() {
  scanf("%d %d\n", &n, &m);
  scanf("%s\n", a);
  scanf("%s\n", b);
  int x = 0;
  for (int i = 0; i < n; ++i) x += (a[i] != b[i]);
  int res = -1;
  for (int t1 = 0; t1 <= min(x, m); ++t1) {
    int t2 = t1;
    int y = x - (t1 + t2);
    if (y < 0) break;
    if (t1 + y <= m) {
      res = t1;
      break;
    }
  }
  if (res == -1) {
    cout << -1;
    return 0;
  }
  int k1 = 0, k2 = 0;
  for (int i = 0; i < n; ++i)
    if (a[i] != b[i]) {
      if (k1 < res)
        s[i] = b[i], k1++;
      else if (k2 < res)
        s[i] = a[i], k2++;
      else {
        for (char j = 'a'; j <= 'z'; ++j)
          if (j != a[i] && j != b[i]) {
            s[i] = j;
            k1++;
            k2++;
            break;
          }
      }
    }
  m -= k1;
  for (int i = 0; i < n; ++i)
    if (a[i] == b[i]) {
      if (m == 0)
        s[i] = a[i];
      else {
        s[i] = a[i] + 1;
        if (s[i] > 'z') s[i] = a[i] - 1;
        m--;
      }
    }
  if (m)
    cout << -1;
  else {
    for (int i = 0; i < n; ++i) printf("%c", s[i]);
  }
  return 0;
}