#include <bits/stdc++.h>
using namespace std;
int chars[30];
vector<char> v;
char nextBig(char c) {
  for (auto el : v) {
    if (c < el) {
      return el;
    }
  }
}
int main() {
  int i, j, n, k;
  string s, t = "";
  scanf("%d %d", &n, &k);
  cin >> s;
  for (i = 0; i < n; i++) {
    if (!chars[s[i] - 'a']) {
      chars[s[i] - 'a'] = 1;
      v.push_back(s[i]);
    }
  }
  sort(v.begin(), v.end());
  for (i = 0; i < min(n, k); i++) {
    t += s[i];
  }
  if (k > n) {
    for (i = 0; i < k - n; i++) {
      t += v[0];
    }
    cout << t << endl;
    return 0;
  }
  for (i = min(n, k) - 1; i >= 0; i--) {
    if (v[v.size() - 1] != t[i]) {
      char c = nextBig(t[i]);
      t[i] = c;
      for (j = i + 1; j < min(n, k); j++) t[j] = v[0];
      cout << t << endl;
      return 0;
    }
  }
  return 0;
}

### Prompt

Please provide a Cpp coded solution to the problem described below:

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 chars[30];
vector<char> v;
char nextBig(char c) {
  for (auto el : v) {
    if (c < el) {
      return el;
    }
  }
}
int main() {
  int i, j, n, k;
  string s, t = "";
  scanf("%d %d", &n, &k);
  cin >> s;
  for (i = 0; i < n; i++) {
    if (!chars[s[i] - 'a']) {
      chars[s[i] - 'a'] = 1;
      v.push_back(s[i]);
    }
  }
  sort(v.begin(), v.end());
  for (i = 0; i < min(n, k); i++) {
    t += s[i];
  }
  if (k > n) {
    for (i = 0; i < k - n; i++) {
      t += v[0];
    }
    cout << t << endl;
    return 0;
  }
  for (i = min(n, k) - 1; i >= 0; i--) {
    if (v[v.size() - 1] != t[i]) {
      char c = nextBig(t[i]);
      t[i] = c;
      for (j = i + 1; j < min(n, k); j++) t[j] = v[0];
      cout << t << endl;
      return 0;
    }
  }
  return 0;
}

```