#include <bits/stdc++.h>
using namespace std;
int n, k;
char s[100005];
bool used[100];
int main() {
  scanf("%d %d", &n, &k);
  scanf("%s", s + 1);
  int minn = 100;
  for (int i = 1; i <= n; i++) minn = min(minn, s[i] - 'a');
  if (k > n) {
    printf("%s", s + 1);
    for (int i = n + 1; i <= k; i++) printf("%c", minn + 'a');
    return 0;
  }
  int maxn = 0;
  for (int i = 1; i <= n; i++) {
    used[s[i] - 'a'] = 1;
    maxn = max(maxn, s[i] - 'a');
  }
  for (int i = k; i >= 1; i--) {
    if (s[i] - 'a' != maxn) {
      for (int j = 1; j < i; j++) printf("%c", s[j]);
      for (int j = s[i] - 'a' + 1; j < 26; j++)
        if (used[j] != 0) {
          printf("%c", j + 'a');
          break;
        }
      for (int j = i + 1; j <= k; j++) printf("%c", minn + 'a');
      return 0;
    }
  }
}

### Prompt

Please formulate a CPP solution to the following problem:

And where the are the phone numbers?

You are given a string s consisting of lowercase English letters and an integer k. Find the lexicographically smallest string t of length k, such that its set of letters is a subset of the set of letters of s and s is lexicographically smaller than t.

It's guaranteed that the answer exists.

Note that the set of letters is a set, not a multiset. For example, the set of letters of abadaba is {a, b, d}.

String p is lexicographically smaller than string q, if p is a prefix of q, is not equal to q or there exists i, such that pi < qi and for all j < i it is satisfied that pj = qj. For example, abc is lexicographically smaller than abcd , abd is lexicographically smaller than abec, afa is not lexicographically smaller than ab and a is not lexicographically smaller than a.

Input

The first line of input contains two space separated integers n and k (1 ≤ n, k ≤ 100 000) — the length of s and the required length of t.

The second line of input contains the string s consisting of n lowercase English letters.

Output

Output the string t conforming to the requirements above.

It's guaranteed that the answer exists.

Examples

Input

3 3
abc


Output

aca


Input

3 2
abc


Output

ac


Input

3 3
ayy


Output

yaa


Input

2 3
ba


Output

baa

Note

In the first example the list of strings t of length 3, such that the set of letters of t is a subset of letters of s is as follows: aaa, aab, aac, aba, abb, abc, aca, acb, .... Among them, those are lexicographically greater than abc: aca, acb, .... Out of those the lexicographically smallest is aca.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
int n, k;
char s[100005];
bool used[100];
int main() {
  scanf("%d %d", &n, &k);
  scanf("%s", s + 1);
  int minn = 100;
  for (int i = 1; i <= n; i++) minn = min(minn, s[i] - 'a');
  if (k > n) {
    printf("%s", s + 1);
    for (int i = n + 1; i <= k; i++) printf("%c", minn + 'a');
    return 0;
  }
  int maxn = 0;
  for (int i = 1; i <= n; i++) {
    used[s[i] - 'a'] = 1;
    maxn = max(maxn, s[i] - 'a');
  }
  for (int i = k; i >= 1; i--) {
    if (s[i] - 'a' != maxn) {
      for (int j = 1; j < i; j++) printf("%c", s[j]);
      for (int j = s[i] - 'a' + 1; j < 26; j++)
        if (used[j] != 0) {
          printf("%c", j + 'a');
          break;
        }
      for (int j = i + 1; j <= k; j++) printf("%c", minn + 'a');
      return 0;
    }
  }
}

```