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 = 100005;
int N, T;
char s1[MaxN], s2[MaxN], s3[MaxN];
inline char other(char c1, char c2) {
  for (char c = 'a'; c <= 'z'; ++c)
    if (c != c1 && c != c2) return c;
}
int main() {
  scanf("%d %d", &N, &T);
  scanf("%s %s", s1, s2);
  int L = 0, C = 0;
  for (int i = 0; i < N; ++i)
    if (s1[i] == s2[i])
      ++C;
    else
      ++L;
  int t = T;
  int L1 = max(0, T - L), R1 = floor((2 * t - L) / 2.0);
  if (R1 < L1) {
    puts("-1");
    return 0;
  }
  if (L1 > C || R1 < 0) {
    puts("-1");
    return 0;
  }
  int b = max(0, L1);
  int x = L - t + b, z = 2 * t - 2 * b - L;
  int y = x;
  for (int i = 0; i < N; ++i)
    if (s1[i] == s2[i]) {
      if (b) {
        printf("%c", other(s1[i], s2[i]));
        --b;
      } else
        printf("%c", s1[i]);
    } else {
      if (x) {
        printf("%c", s1[i]);
        --x;
      } else {
        if (y) {
          printf("%c", s2[i]);
          --y;
        } else
          printf("%c", other(s1[i], s2[i]));
      }
    }
  puts("");
  return 0;
}