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 double eps = 1e-8;
const double pi = acos(-1.0);
template <class T>
int chkmin(T &a, T b) {
  return a > b ? a = b, 1 : 0;
}
template <class T>
int chkmax(T &a, T b) {
  return a < b ? a = b, 1 : 0;
}
template <class T>
T sqr(T a) {
  return a * a;
}
template <class T>
T mmin(T a, T b) {
  return a < b ? a : b;
}
template <class T>
T mmax(T a, T b) {
  return a > b ? a : b;
}
template <class T>
T aabs(T a) {
  return a < 0 ? -a : a;
}
int read() {
  int s = 0, base = 1;
  char c;
  while (!isdigit(c = getchar()))
    if (c == '-') base = -base;
  while (isdigit(c)) {
    s = s * 10 + (c ^ 48);
    c = getchar();
  }
  return s * base;
}
char WriteIntBuffer[1024];
template <class T>
void write(T a, char end) {
  int cnt = 0, fu = 1;
  if (a < 0) {
    putchar('-');
    fu = -1;
  }
  do {
    WriteIntBuffer[++cnt] = fu * (a % 10) + '0';
    a /= 10;
  } while (a);
  while (cnt) {
    putchar(WriteIntBuffer[cnt]);
    --cnt;
  }
  putchar(end);
}
char s[192608];
void get_(char *s) {
  while (!isalpha(*s = getchar()))
    ;
  while (isalpha(*s)) *(++s) = getchar();
  *s = 0;
}
int cnt[27];
char fa[192608];
int JS(int pos, int k) {
  if (!s[pos]) {
    int i;
    for (i = 0; !cnt[i]; ++i)
      ;
    while (pos < k) {
      fa[pos] = i + 'a';
      ++pos;
    }
    fa[pos] = 0;
    return 1;
  }
  if (pos == k - 1) {
    int i = s[pos] - 'a' + 1;
    while (i < 26 && !cnt[i]) ++i;
    if (i < 26) {
      fa[pos] = i + 'a';
      fa[pos + 1] = 0;
      return 1;
    } else
      return 0;
  } else {
    int sg = JS(pos + 1, k);
    if (sg) {
      fa[pos] = s[pos];
      return 1;
    } else {
      int i = s[pos] - 'a' + 1;
      while (i < 26 && !cnt[i]) ++i;
      if (i < 26) {
        fa[pos] = i + 'a';
        i = 0;
        while (!cnt[i]) ++i;
        while (++pos < k) fa[pos] = i + 'a';
        fa[pos + 1] = 0;
        return 1;
      } else
        return 0;
    }
  }
}
int main() {
  int n, k;
  n = read();
  k = read();
  get_(s);
  for (int i = 0; s[i]; ++i) cnt[s[i] - 'a'] = 1;
  JS(0, k);
  printf("%s\n", fa);
  return 0;
}
