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 int MAXN = 100000 + 50;
int n, t, same, diff;
char s1[MAXN], s2[MAXN], s3[MAXN];
int main() {
  scanf("%d%d", &n, &t);
  scanf("%s%s", s1, s2);
  for (int i = 0; s1[i]; i++) {
    same += s1[i] == s2[i];
    diff += s1[i] != s2[i];
  }
  if (t < (diff + 1) / 2)
    printf("-1\n");
  else {
    int len = strlen(s1);
    for (int i = 0; i < len; i++) s3[i] = s1[i];
    for (int i = 0; i < len; i++)
      if (s1[i] != s2[i])
        while (s3[i] == s2[i] || s3[i] == s1[i])
          s3[i] = (s3[i] - 'a' + 27) % 26 + 'a';
    if (t >= diff) {
      int clk = t - diff;
      for (int i = 0; i < len && clk; i++)
        if (s1[i] == s2[i]) {
          s3[i] = (s3[i] - 'a' + 27) % 26 + 'a';
          clk--;
        }
    } else {
      int clk = diff - t, cnt = 0;
      for (int i = 0; i < len && cnt < clk * 2; i++)
        if (s1[i] != s2[i]) {
          if (cnt < clk)
            s3[i] = s2[i];
          else
            s3[i] = s1[i];
          cnt++;
        }
    }
    s3[len] = 0;
    printf("%s\n", s3);
  }
  return 0;
}