#include <bits/stdc++.h>
using namespace std;
const long long MAXN = 2e5 + 5, INF = 9e13, MOD = 1e9 + 7;
long long n, k, a;
string s, ans;
char c, mic = 'z';
bool b[30];
int main() {
  cin >> n >> k >> s;
  mic = s[0];
  for (int i = 0; i < s.length(); i++) {
    mic = min(mic, s[i]);
    c = max(c, s[i]);
    b[int(s[i] - 'a')] = 1;
  }
  ans = s;
  while (ans.length() < k) ans += mic;
  if (k > n) {
    cout << ans;
    return 0;
  }
  int i;
  for (i = k - 1; s[i] == c; i--) ans[i] = mic;
  for (int j = 0; j < 28; j++) {
    if (b[j] && j > int(s[i] - 'a')) {
      ans[i] = char(j + 'a');
      break;
    }
  }
  for (int j = 0; j < k; j++) cout << ans[j];
  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;
const long long MAXN = 2e5 + 5, INF = 9e13, MOD = 1e9 + 7;
long long n, k, a;
string s, ans;
char c, mic = 'z';
bool b[30];
int main() {
  cin >> n >> k >> s;
  mic = s[0];
  for (int i = 0; i < s.length(); i++) {
    mic = min(mic, s[i]);
    c = max(c, s[i]);
    b[int(s[i] - 'a')] = 1;
  }
  ans = s;
  while (ans.length() < k) ans += mic;
  if (k > n) {
    cout << ans;
    return 0;
  }
  int i;
  for (i = k - 1; s[i] == c; i--) ans[i] = mic;
  for (int j = 0; j < 28; j++) {
    if (b[j] && j > int(s[i] - 'a')) {
      ans[i] = char(j + 'a');
      break;
    }
  }
  for (int j = 0; j < k; j++) cout << ans[j];
  return 0;
}

```