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 main() {
  int n, t;
  cin >> n >> t;
  string s1, s2;
  cin >> s1 >> s2;
  int same = 0;
  for (int i = 0; i < n; i++) {
    if (s1[i] == s2[i]) {
      ++same;
    }
  }
  int diff = n - same;
  int low = (diff + 1) / 2;
  int high = low + same;
  if (t < low) {
    puts("-1");
    return 0;
  }
  int a = 0;
  int b = 0;
  string ans = s1;
  if (t >= diff) {
    for (int i = 0; i < n; i++) {
      if (s1[i] != s2[i]) {
        if (s1[i] != 'a' && s2[i] != 'a') {
          ans[i] = 'a';
        }
        if (s1[i] != 'b' && s2[i] != 'b') {
          ans[i] = 'b';
        }
        if (s1[i] != 'c' && s2[i] != 'c') {
          ans[i] = 'c';
        }
      }
    }
    t -= diff;
    for (int i = 0; i < n; i++) {
      if (s1[i] == s2[i]) {
        if (t == 0) {
          ans[i] = s1[i];
        } else {
          --t;
          if (s1[i] == 'a') {
            ans[i] = 'b';
          } else {
            ans[i] = 'a';
          }
        }
      }
    }
  } else {
    int sam = n - t;
    for (int i = 0; i < n; i++) {
      if (s1[i] == s2[i]) {
        ans[i] = s1[i];
        --sam;
      }
    }
    bool f = false;
    for (int i = 0; i < n; i++) {
      if (s1[i] != s2[i]) {
        if (f) {
          ans[i] = s2[i];
          f = false;
        } else {
          if (sam) {
            --sam;
            f = true;
            ans[i] = s1[i];
          } else {
            if (s1[i] != 'a' && s2[i] != 'a') {
              ans[i] = 'a';
            }
            if (s1[i] != 'b' && s2[i] != 'b') {
              ans[i] = 'b';
            }
            if (s1[i] != 'c' && s2[i] != 'c') {
              ans[i] = 'c';
            }
          }
        }
      }
    }
  }
  cout << ans << endl;
  return 0;
}