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.
#include <bits/stdc++.h>
using namespace std;
vector<char> GetAlphabet(const string &str) {
  vector<bool> used(26, false);
  for (const auto &ch : str) {
    used[ch - 'a'] = true;
  }
  vector<char> alpha;
  for (int i = 0; i < 26; ++i) {
    if (used[i]) {
      alpha.push_back('a' + i);
    }
  }
  return alpha;
}
vector<int> GetIndexes(const string &str, const vector<char> &alpha, int len) {
  vector<int> index(26, -1);
  for (int i = 0; i < (int)alpha.size(); ++i) {
    index[alpha[i] - 'a'] = i;
  }
  vector<int> res(len);
  for (int i = 0; i < len; ++i) {
    res[i] = index[str[i] - 'a'];
  }
  return res;
}
string GetFromIndexes(const vector<int> &ind, const vector<char> &alpha) {
  string str(ind.size(), 0);
  for (int i = 0; i < (int)ind.size(); ++i) {
    str[i] = alpha[ind[i]];
  }
  return str;
}
int main() {
  int n, m;
  cin >> n >> m;
  cin.get();
  string str;
  getline(cin, str);
  auto alpha = GetAlphabet(str);
  if (m > n) {
    str.resize(m, alpha[0]);
    cout << str << "\n";
    return 0;
  }
  auto vec = GetIndexes(str, alpha, m);
  int ind = m - 1;
  while (ind > 0 && vec[ind] == (int)alpha.size() - 1) {
    vec[ind] = 0;
    ind -= 1;
  }
  vec[ind] += 1;
  cout << GetFromIndexes(vec, alpha) << "\n";
  return 0;
}
