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;
char s1[100005], s2[100005], s3[100005];
int diff;
int currdiff;
void MakeMin() {
  for (int i = 0; i <= n - 1; i++) {
    if (currdiff == diff - 1 && diff % 2 == 1) {
      if (s1[i] != 'a' && s2[i] != 'a') s3[i] = 'a';
      if (s1[i] != 'b' && s2[i] != 'b') s3[i] = 'b';
      if (s1[i] != 'c' && s2[i] != 'c') s3[i] = 'c';
    } else if (s1[i] != s2[i]) {
      if (currdiff < diff / 2)
        s3[i] = s1[i];
      else
        s3[i] = s2[i];
      currdiff++;
    }
  }
  currdiff /= 2;
  currdiff += (diff % 2);
  s3[n] = '\0';
}
void Double(int x) {
  int cnt1 = 0;
  int cnt2 = 0;
  for (int i = 0; i <= n - 1; i++) {
    if (s1[i] != s2[i] && s1[i] == s3[i]) {
      if (cnt1 == x) continue;
      if (s1[i] != 'a' && s2[i] != 'a') s3[i] = 'a';
      if (s1[i] != 'b' && s2[i] != 'b') s3[i] = 'b';
      if (s1[i] != 'c' && s2[i] != 'c') s3[i] = 'c';
      cnt1++;
    }
    if (s1[i] != s2[i] && s2[i] == s3[i]) {
      if (cnt2 == x) continue;
      if (s1[i] != 'a' && s2[i] != 'a') s3[i] = 'a';
      if (s1[i] != 'b' && s2[i] != 'b') s3[i] = 'b';
      if (s1[i] != 'c' && s2[i] != 'c') s3[i] = 'c';
      cnt2++;
    }
  }
}
void Fuk(int x) {
  for (int i = 0; i <= n - 1; i++) {
    if (s1[i] == s2[i]) {
      if (x > 0) {
        if (s1[i] == 'a')
          s3[i] = 'b';
        else
          s3[i] = 'a';
        x--;
      } else
        s3[i] = s1[i];
    }
  }
}
int main() {
  scanf("%d %d", &n, &t);
  scanf("%s", s1);
  scanf("%s", s2);
  for (int i = 0; i <= n - 1; i++) {
    if (s1[i] != s2[i]) diff++;
  }
  MakeMin();
  if (t < currdiff) {
    cout << -1;
    return 0;
  }
  int T = t - currdiff;
  Double(min(T, diff / 2));
  T -= min(T, diff / 2);
  Fuk(T);
  cout << s3 << endl;
  return 0;
}