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;
char a[1000000], b[1000000], res[1000000];
bool diff[1000000];
set<int> diffs;
void DeleteDiff1(int cur, int n) {
  int f = cur;
  int s = cur;
  for (int i = 0; i < n; i++) {
    if (a[i] != b[i]) {
      if (f > 0) {
        res[i] = a[i];
        f--;
        continue;
      }
      if (s > 0) {
        res[i] = b[i];
        s--;
      }
    }
  }
}
void DeleteDiff2(int cur, int n) {
  for (int i = 0; i<n, cur> 0; i++) {
    if (a[i] == b[i]) {
      res[i] = b[i];
      cur--;
    }
  }
}
void DiffStr(int n) {
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < 3; j++) {
      char curS = j + 'a';
      if (curS == a[i] || curS == b[i]) continue;
      res[i] = curS;
      break;
    }
  }
}
int main() {
  int n, t;
  scanf("%d%d", &n, &t);
  char c;
  for (int i = 0; i < n; i++) {
    scanf("%c", &c);
    if (c == '\n') {
      i--;
      continue;
    }
    a[i] = c;
  }
  for (int i = 0; i < n; i++) {
    scanf("%c", &c);
    if (c == '\n') {
      i--;
      continue;
    }
    b[i] = c;
  }
  int curDiff = 0;
  int curEqual = n - curDiff;
  for (int i = 0; i < n; i++) {
    diff[i] = (a[i] != b[i]);
    curDiff += (a[i] != b[i]);
    if (a[i] != b[i]) diffs.insert(i);
  }
  int minDiff = curDiff / 2 + curDiff % 2;
  if (t < minDiff) {
    printf("-1");
    return 0;
  }
  DiffStr(n);
  DeleteDiff2(n - max(t, curDiff), n);
  if (t < curDiff) DeleteDiff1(curDiff - t, n);
  for (int i = 0; i < n; i++) {
    printf("%c", res[i]);
  }
  return 0;
}