#include <bits/stdc++.h>
using namespace std;
const int N = 1e5 + 10;
const long long INF = 0x3f3f3f3f3f3f3f3f;
char s[N], ans[N];
bool vis[30];
int main() {
  int n, k;
  scanf("%d %d %s", &n, &k, s);
  for (int i = 0; i < n; i++) vis[s[i] - 'a'] = 1;
  char mi;
  for (int i = 0; i < 26; i++)
    if (vis[i]) {
      mi = i + 'a';
      break;
    }
  int pos;
  ans[k] = '\000';
  for (int i = k - 1; i >= 0; i--) {
    bool ok = 0;
    char c;
    for (int j = max(0, (s[i] - 'a') + 1); j < 26; j++)
      if (vis[j]) {
        ok = 1;
        c = j + 'a';
        break;
      }
    if (ok) {
      ans[i] = c;
      pos = i;
      break;
    } else
      ans[i] = mi;
  }
  for (int i = pos - 1; i >= 0; i--) ans[i] = (i >= n ? mi : s[i]);
  printf("%s\n", ans);
  return 0;
}

### Prompt

Your task is to create 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;
const int N = 1e5 + 10;
const long long INF = 0x3f3f3f3f3f3f3f3f;
char s[N], ans[N];
bool vis[30];
int main() {
  int n, k;
  scanf("%d %d %s", &n, &k, s);
  for (int i = 0; i < n; i++) vis[s[i] - 'a'] = 1;
  char mi;
  for (int i = 0; i < 26; i++)
    if (vis[i]) {
      mi = i + 'a';
      break;
    }
  int pos;
  ans[k] = '\000';
  for (int i = k - 1; i >= 0; i--) {
    bool ok = 0;
    char c;
    for (int j = max(0, (s[i] - 'a') + 1); j < 26; j++)
      if (vis[j]) {
        ok = 1;
        c = j + 'a';
        break;
      }
    if (ok) {
      ans[i] = c;
      pos = i;
      break;
    } else
      ans[i] = mi;
  }
  for (int i = pos - 1; i >= 0; i--) ans[i] = (i >= n ? mi : s[i]);
  printf("%s\n", ans);
  return 0;
}

```