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;
const int mod = 1e9 + 7;
template <class T, class U>
inline void add_self(T &a, U b) {
  a += b;
  if (a >= mod) a -= mod;
  if (a < 0) a += mod;
}
template <class T, class U>
inline void min_self(T &x, U y) {
  if (y < x) x = y;
}
template <class T, class U>
inline void max_self(T &x, U y) {
  if (y > x) x = y;
}
void _print() { cerr << "]\n"; }
template <typename T, typename... V>
void _print(T t, V... v) {
  cout << t;
  ;
  if (sizeof...(v)) cerr << ", ";
  _print(v...);
}
template <class T, class U>
void print_m(const map<T, U> &m, int w = 3) {
  if (m.empty()) {
    cout << "Empty" << endl;
    return;
  }
  for (auto x : m) cout << "(" << x.first << ": " << x.second << ")," << endl;
  cout << endl;
}
template <class T, class U>
void debp(const pair<T, U> &pr, bool end_line = 1) {
  cout << "{" << pr.first << " " << pr.second << "}";
  cout << (end_line ? "\n" : ", ");
}
template <class T>
void print_vp(const T &vp, int sep_line = 0) {
  if (vp.empty()) {
    cout << "Empty" << endl;
    return;
  }
  if (!sep_line) cout << "{ ";
  for (auto x : vp) debp(x, sep_line);
  if (!sep_line) cout << "}\n";
  cout << endl;
}
template <typename T>
void print(const T &v, bool show_index = false) {
  int w = 2;
  if (show_index) {
    for (int i = 0; i < int((v).size()); i++) cout << setw(w) << i << " ";
    cout << endl;
  }
  for (auto &el : v) cout << setw(w) << el << " ";
  cout << endl;
}
template <typename T>
void print_vv(const T &vv) {
  if (int((vv).size()) == 0) {
    cout << "Empty" << endl;
    return;
  }
  int w = 3;
  cout << setw(w) << " ";
  for (int j = 0; j < int((*vv.begin()).size()); j++)
    cout << setw(w) << j << " ";
  cout << endl;
  int i = 0;
  for (auto &v : vv) {
    cout << i++ << " {";
    for (auto &el : v) cout << setw(w) << el << " ";
    cout << "},\n";
  }
  cout << endl;
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  int n, k;
  while (cin >> n >> k) {
    string s;
    cin >> s;
    set<char> st;
    for (auto x : s) st.insert(x);
    char mx = *(--st.end());
    char mn = *(st.begin());
    if (k > n) {
      int ex = k - n;
      for (int i = 0; i < int(ex); i++) s += mn;
      cout << s << endl;
    } else if (k == n) {
      int i = n - 1;
      for (; i >= 0; --i) {
        if (s[i] != mx) {
          s[i] = *st.upper_bound(s[i]);
          for (int j = i + 1; j < n; ++j) s[j] = mn;
          break;
        }
      }
      cout << s << endl;
    } else {
      int i = k - 1;
      for (; i >= 0; --i) {
        if (s[i] != mx) {
          s[i] = *st.upper_bound(s[i]);
          for (int j = i + 1; j < n; ++j) s[j] = mn;
          break;
        }
      }
      for (int i = 0; i < k; ++i) cout << s[i];
      cout << endl;
    }
  }
  return 0;
}
