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 T, N;
int main() {
  string s1, s2;
  cin >> N >> T;
  cin >> s1 >> s2;
  char s3[100100];
  int t1 = T, t2 = T;
  for (int i = 0; i < N; i++) {
    if (s1[i] != s2[i]) {
      if (t2 >= t1) {
        s3[i] = s1[i];
        t2--;
      } else {
        s3[i] = s2[i];
        t1--;
      }
    } else {
      s3[i] = s1[i];
    }
  }
  if ((t1 < 0) || (t2 < 0)) {
    cout << -1;
    return 0;
  } else {
    for (int i = 0; i < N; i++) {
      if (s1[i] == s2[i]) {
        if ((t1 > 0) && (t2 > 0)) {
          char c;
          if (('a' <= s1[i] + 1) && (s1[i] + 1 <= 'z')) {
            c = (char)(s1[i] + 1);
          } else {
            c = (char)(s1[i] - 1);
          }
          s3[i] = c;
          t1--;
          t2--;
        } else {
          s3[i] = s1[i];
        }
      }
    }
  }
  if (t1 > 0 || t2 > 0) {
    for (int i = 0; i < N; i++) {
      if ((t1 > 0) && (s3[i] == s1[i]) && (s2[i] != s1[i])) {
        for (char c = 'a'; c <= 'z'; c++) {
          if (c != s1[i] && c != s2[i]) {
            s3[i] = c;
            break;
          }
        }
        t1--;
      } else if ((t2 > 0) && (s3[i] == s2[i]) && (s2[i] != s1[i])) {
        for (char c = 'a'; c <= 'z'; c++) {
          if (c != s1[i] && c != s2[i]) {
            s3[i] = c;
            break;
          }
        }
        t2--;
      }
    }
    if (t1 > 0 || t2 > 0) {
      cout << -1;
      return 0;
    } else {
      for (int i = 0; i < N; i++) cout << s3[i];
    }
  } else {
    for (int i = 0; i < N; i++) cout << s3[i];
  }
  return 0;
}