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.
(n,k) = map(int, raw_input().strip().split(' '))
s = raw_input().strip()

sset = set(s)
slist = list(sset)
slist.sort()
nextbiggest = {}
for i in range(len(slist)-1):
  nextbiggest[slist[i]] = slist[i+1]
  
newstring = ""
if k > n:
  newstring = s + (slist[0]*(k-n))
else:
  while k > 0:
    if s[k-1] == slist[-1]:
      newstring = slist[0] + newstring
    else:
      newstring = nextbiggest[s[k-1]] + newstring
      break
    k -= 1
  newstring = s[0:k-1] + newstring
  
print newstring
  