#include <bits/stdc++.h>
using namespace std;
#pragma comment(linker, "/STACK:667177216")
const long long mod = 1000000007;
int n, k;
vector<char> tmp;
set<char> st;
string s;
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cin >> n >> k;
  cin >> s;
  for (int i = 0; i < s.size(); i++) {
    st.insert(s[i]);
  }
  if (k > n) {
    string t = s;
    while (k > n) {
      s += *st.begin();
      k--;
    }
    cout << s << '\n';
    return 0;
  }
  string t = s.substr(0, k);
  for (int i = t.size() - 1; i >= 0; i--) {
    if (t[i] != *st.rbegin()) {
      t[i] = *st.upper_bound(t[i]);
      for (int j = i + 1; j < t.size(); j++) {
        t[j] = *st.begin();
      }
      cout << t << '\n';
      return 0;
    }
  }
  return 0;
}

### Prompt

Construct a CPP code solution to the problem outlined:

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;
#pragma comment(linker, "/STACK:667177216")
const long long mod = 1000000007;
int n, k;
vector<char> tmp;
set<char> st;
string s;
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cin >> n >> k;
  cin >> s;
  for (int i = 0; i < s.size(); i++) {
    st.insert(s[i]);
  }
  if (k > n) {
    string t = s;
    while (k > n) {
      s += *st.begin();
      k--;
    }
    cout << s << '\n';
    return 0;
  }
  string t = s.substr(0, k);
  for (int i = t.size() - 1; i >= 0; i--) {
    if (t[i] != *st.rbegin()) {
      t[i] = *st.upper_bound(t[i]);
      for (int j = i + 1; j < t.size(); j++) {
        t[j] = *st.begin();
      }
      cout << t << '\n';
      return 0;
    }
  }
  return 0;
}

```