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.
#include <bits/stdc++.h>
using namespace std;
const long long MAXN = 5e5 + 100;
const long long MOD = 1e9 + 7;
bool setc[30];
char str[MAXN];
int main(int argc, char const *argv[]) {
  long long len, lena;
  while (cin >> len >> lena) {
    memset(setc, 0, sizeof setc);
    scanf("%s", str);
    for (int i = 0; i < len; ++i) setc[str[i] - 'a'] = 1;
    long long minc;
    for (int i = 0; i < 26; ++i)
      if (setc[i]) {
        minc = i;
        break;
      }
    if (lena > len) {
      for (int i = len; i < lena; ++i) str[i] = minc + 'a';
      str[lena] = '\0';
      printf("%s\n", str);
      continue;
    }
    str[lena] = '\0';
    long long maxc;
    for (int i = 25; i >= 0; --i)
      if (setc[i]) {
        maxc = i;
        break;
      }
    for (int i = lena - 1; i >= 0; --i)
      if (maxc > str[i] - 'a') {
        for (int j = str[i] - 'a' + 1; j < 26; ++j)
          if (setc[j]) {
            str[i] = j + 'a';
            break;
          }
        for (int j = i + 1; j < lena; ++j) str[j] = minc + 'a';
        break;
      }
    printf("%s\n", str);
  }
  return 0;
}
