#include <bits/stdc++.h>
using namespace std;
set<int> x;
int main() {
  int n, m;
  cin >> n >> m;
  string s;
  cin >> s;
  char c[100000];
  for (int i = 0; i < n; i++) {
    x.insert(s[i] - 97);
  }
  int l;
  if (m > n) {
    l = m - n;
    cout << s;
    for (int i = n + l - 1; i >= n; i--) {
      set<int>::iterator f = x.begin();
      cout << (char)(*f + 97);
    }
  } else if (m <= n) {
    set<int>::iterator f = x.begin();
    set<int>::iterator z = x.end();
    z--;
    int l = -1;
    for (int i = m - 1; i >= 0; i--) {
      if (s[i] - 97 == *z) {
        s[i] = (char)(*f + 97);
      } else {
        int l = *x.upper_bound(s[i] - 97);
        s[i] = (char)(l + 97);
        break;
      }
    }
    for (int i = 0; i < m; i++) cout << s[i];
  }
  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;
set<int> x;
int main() {
  int n, m;
  cin >> n >> m;
  string s;
  cin >> s;
  char c[100000];
  for (int i = 0; i < n; i++) {
    x.insert(s[i] - 97);
  }
  int l;
  if (m > n) {
    l = m - n;
    cout << s;
    for (int i = n + l - 1; i >= n; i--) {
      set<int>::iterator f = x.begin();
      cout << (char)(*f + 97);
    }
  } else if (m <= n) {
    set<int>::iterator f = x.begin();
    set<int>::iterator z = x.end();
    z--;
    int l = -1;
    for (int i = m - 1; i >= 0; i--) {
      if (s[i] - 97 == *z) {
        s[i] = (char)(*f + 97);
      } else {
        int l = *x.upper_bound(s[i] - 97);
        s[i] = (char)(l + 97);
        break;
      }
    }
    for (int i = 0; i < m; i++) cout << s[i];
  }
  return 0;
}

```