#include <bits/stdc++.h>
using namespace std;
int32_t main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  ;
  long long n, k;
  cin >> n >> k;
  string s;
  cin >> s;
  vector<long long> v(26);
  for (long long i = 0; i < n; i++) {
    v[s[i] - 'a']++;
  }
  if (n < k) {
    cout << s;
    for (long long i = 0; i < 26; i++) {
      if (v[i]) {
        long long t = k - n;
        while (t--) cout << char('a' + i);
        return 0;
      }
    }
  }
  string ans;
  for (long long i = k - 1; i >= 0; i--) {
    long long p = s[i] - 'a';
    for (long long j = p + 1; j < 26; j++) {
      if (v[j]) {
        for (long long x = 0; x < i; x++) {
          cout << s[x];
        }
        cout << char(j + 'a');
        long long x = k - 1 - i;
        for (long long d = 0; d < 26; d++) {
          if (v[d]) {
            for (long long g = 0; g < x; g++) {
              cout << char('a' + d);
            }
            return 0;
          }
        }
      }
    }
  }
  return 0;
}

### Prompt

Please create a solution in CPP 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;
int32_t main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  ;
  long long n, k;
  cin >> n >> k;
  string s;
  cin >> s;
  vector<long long> v(26);
  for (long long i = 0; i < n; i++) {
    v[s[i] - 'a']++;
  }
  if (n < k) {
    cout << s;
    for (long long i = 0; i < 26; i++) {
      if (v[i]) {
        long long t = k - n;
        while (t--) cout << char('a' + i);
        return 0;
      }
    }
  }
  string ans;
  for (long long i = k - 1; i >= 0; i--) {
    long long p = s[i] - 'a';
    for (long long j = p + 1; j < 26; j++) {
      if (v[j]) {
        for (long long x = 0; x < i; x++) {
          cout << s[x];
        }
        cout << char(j + 'a');
        long long x = k - 1 - i;
        for (long long d = 0; d < 26; d++) {
          if (v[d]) {
            for (long long g = 0; g < x; g++) {
              cout << char('a' + d);
            }
            return 0;
          }
        }
      }
    }
  }
  return 0;
}

```