#include <bits/stdc++.h>
using namespace std;
int n, k;
char str[100005];
int a[35];
int m[35];
int main() {
  cin >> n >> k;
  cin >> str;
  int c = 0;
  int len = strlen(str);
  for (int i = 0; i < len; i++) {
    if (m[str[i] - 'a'] == 0) {
      m[str[i] - 'a'] = 1;
      a[c++] = str[i] - 'a';
    }
  }
  sort(a, a + c);
  if (n < k) {
    cout << str;
    k -= len;
    while (k--) cout << (char)('a' + a[0]);
    cout << endl;
    return 0;
  }
  for (int i = k - 1; i >= 0; i--) {
    if (str[i] - 'a' == a[c - 1]) {
      str[i] = a[0] + 'a';
    } else {
      for (int j = 0; j < c; j++) {
        if (str[i] - 'a' == a[j]) {
          str[i] = a[j + 1] + 'a';
          break;
        }
      }
      break;
    }
  }
  for (int i = 0; i < k; i++) {
    printf("%c", str[i]);
  }
  cout << endl;
}

### 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;
int n, k;
char str[100005];
int a[35];
int m[35];
int main() {
  cin >> n >> k;
  cin >> str;
  int c = 0;
  int len = strlen(str);
  for (int i = 0; i < len; i++) {
    if (m[str[i] - 'a'] == 0) {
      m[str[i] - 'a'] = 1;
      a[c++] = str[i] - 'a';
    }
  }
  sort(a, a + c);
  if (n < k) {
    cout << str;
    k -= len;
    while (k--) cout << (char)('a' + a[0]);
    cout << endl;
    return 0;
  }
  for (int i = k - 1; i >= 0; i--) {
    if (str[i] - 'a' == a[c - 1]) {
      str[i] = a[0] + 'a';
    } else {
      for (int j = 0; j < c; j++) {
        if (str[i] - 'a' == a[j]) {
          str[i] = a[j + 1] + 'a';
          break;
        }
      }
      break;
    }
  }
  for (int i = 0; i < k; i++) {
    printf("%c", str[i]);
  }
  cout << endl;
}

```