#include <bits/stdc++.h>
using namespace std;
int n, k, j, x, i, f[26];
string s;
int main() {
  cin >> n >> k;
  cin >> s;
  for (i = 0; i < s.size(); i++) f[s[i] - 'a'] = 1;
  if (k > n) {
    cout << s;
    j = 0;
    while (j < 26 && !f[j]) j++;
    while (n < k) {
      cout << char(j + 'a');
      n++;
    }
    return 0;
  }
  for (i = k - 1; i >= 0; i--) {
    j = s[i] - 'a' + 1;
    while (j < 26 && !f[j]) j++;
    if (j < 26) {
      for (x = 0; x < i; x++) cout << s[x];
      cout << char(j + 'a');
      j = 0;
      while (j < 26 && !f[j]) j++;
      for (x = i + 1; x < k; x++) cout << char(j + 'a');
      cout << endl;
      return 0;
    }
  }
}

### Prompt

Please create a solution in Cpp 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, j, x, i, f[26];
string s;
int main() {
  cin >> n >> k;
  cin >> s;
  for (i = 0; i < s.size(); i++) f[s[i] - 'a'] = 1;
  if (k > n) {
    cout << s;
    j = 0;
    while (j < 26 && !f[j]) j++;
    while (n < k) {
      cout << char(j + 'a');
      n++;
    }
    return 0;
  }
  for (i = k - 1; i >= 0; i--) {
    j = s[i] - 'a' + 1;
    while (j < 26 && !f[j]) j++;
    if (j < 26) {
      for (x = 0; x < i; x++) cout << s[x];
      cout << char(j + 'a');
      j = 0;
      while (j < 26 && !f[j]) j++;
      for (x = i + 1; x < k; x++) cout << char(j + 'a');
      cout << endl;
      return 0;
    }
  }
}

```