#include <bits/stdc++.h>
using namespace std;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  int n, k;
  cin >> n >> k;
  string s;
  cin >> s;
  map<char, int> st;
  for (auto it : s) {
    st[it] = 1;
  }
  int num = 0;
  vector<char> get(st.size());
  for (auto &it : st) {
    it.second = num;
    get[num++] = it.first;
  }
  if (n >= k) {
    vector<int> a(k);
    for (int i = 0; i < k; i++) a[i] = st[s[i]];
    a[k - 1]++;
    for (int i = k - 1; i > 0; i--) {
      a[i - 1] += (a[i] / (st.size()));
      a[i] %= (st.size());
    }
    for (auto it : a) {
      cout << get[it];
    }
    cout << endl;
  } else {
    cout << s;
    for (int i = 0; i < k - n; i++) {
      cout << get[0];
    }
    cout << endl;
  }
  return 0;
}

### Prompt

Your challenge is to write 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;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  int n, k;
  cin >> n >> k;
  string s;
  cin >> s;
  map<char, int> st;
  for (auto it : s) {
    st[it] = 1;
  }
  int num = 0;
  vector<char> get(st.size());
  for (auto &it : st) {
    it.second = num;
    get[num++] = it.first;
  }
  if (n >= k) {
    vector<int> a(k);
    for (int i = 0; i < k; i++) a[i] = st[s[i]];
    a[k - 1]++;
    for (int i = k - 1; i > 0; i--) {
      a[i - 1] += (a[i] / (st.size()));
      a[i] %= (st.size());
    }
    for (auto it : a) {
      cout << get[it];
    }
    cout << endl;
  } else {
    cout << s;
    for (int i = 0; i < k - n; i++) {
      cout << get[0];
    }
    cout << endl;
  }
  return 0;
}

```