#include <bits/stdc++.h>
using namespace std;
void solve() {
  int n, k;
  cin >> n >> k;
  string s;
  cin >> s;
  set<char> ST;
  for (char x : s) ST.insert(x);
  if (k > n) {
    for (int i = 0; i < n; i++) cout << s[i];
    for (int i = n; i < k; i++) cout << *ST.begin();
    return;
  }
  for (int i = k - 1; i >= 0; i--) {
    if (s[i] < *ST.rbegin()) {
      string f = "";
      for (int j = 0; j < i; j++) f += s[j];
      char mnThatWorkz = 'z';
      for (char c : ST) {
        if (c > s[i] && mnThatWorkz > c) mnThatWorkz = c;
      }
      f += mnThatWorkz;
      while ((int)f.size() < k) f += *ST.begin();
      cout << f << "\n";
      return;
    }
  }
}
int32_t main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  ;
  int t = 1;
  while (t--) {
    solve();
  }
}

### Prompt

Your task is to create 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;
void solve() {
  int n, k;
  cin >> n >> k;
  string s;
  cin >> s;
  set<char> ST;
  for (char x : s) ST.insert(x);
  if (k > n) {
    for (int i = 0; i < n; i++) cout << s[i];
    for (int i = n; i < k; i++) cout << *ST.begin();
    return;
  }
  for (int i = k - 1; i >= 0; i--) {
    if (s[i] < *ST.rbegin()) {
      string f = "";
      for (int j = 0; j < i; j++) f += s[j];
      char mnThatWorkz = 'z';
      for (char c : ST) {
        if (c > s[i] && mnThatWorkz > c) mnThatWorkz = c;
      }
      f += mnThatWorkz;
      while ((int)f.size() < k) f += *ST.begin();
      cout << f << "\n";
      return;
    }
  }
}
int32_t main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  ;
  int t = 1;
  while (t--) {
    solve();
  }
}

```