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 long long MOD = 1000000007;
char a[100007], b[100007];
char ans[100007];
bool used[100007];
char go(char c) {
  c++;
  if (c > 'z') {
    c = 'a';
  }
  return c;
}
char go(char a, char b) {
  a = go(a);
  if (a == b) a = go(a);
  return a;
}
int main() {
  int n, m;
  scanf("%d%d", &n, &m);
  scanf("%s", a);
  scanf("%s", b);
  int have = 0;
  for (int i = 0; i < n; i++) {
    if (a[i] != b[i]) {
      have++;
    }
  }
  int ans1 = -1;
  int more = -1;
  for (int i = 0; i <= have; i++) {
    if (2 * i > have) continue;
    int add = have - i;
    if (add <= m && m - add <= n - have) {
      ans1 = i;
      more = m - add;
      break;
    }
  }
  if (ans1 == -1) {
    printf("-1\n");
    return 0;
  }
  ans1 *= 2;
  int go1 = ans1;
  for (int i = 0; i < n; i++) {
    if (a[i] != b[i] && go1 > 0) {
      if (go1 % 2 == 0) {
        ans[i] = a[i];
      } else {
        ans[i] = b[i];
      }
      go1--;
      used[i] = true;
    }
  }
  for (int i = 0; i < n; i++) {
    if (used[i]) continue;
    if (a[i] != b[i]) {
      ans[i] = go(a[i], b[i]);
    } else if (more > 0) {
      ans[i] = go(a[i]);
      more--;
    } else {
      ans[i] = a[i];
    }
  }
  int ta = 0, tb = 0;
  for (int i = 0; i < n; i++) {
    if (a[i] != ans[i]) ta++;
    if (b[i] != ans[i]) tb++;
  }
  if (ta != m || tb != m) {
    printf("-1\n");
    return 0;
  }
  for (int i = 0; i < n; i++) {
    printf("%c", ans[i]);
  }
  printf("\n");
}