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  = raw_input().split(" ")
n = int(n)
k = int(k)
s = str(raw_input())
j = 0
result = ""
min_letter = 122  
max_letter = 97
lex = [0]*26
for i in s:
	lex[ord(i) - 97] = 1
	if ord(i)  > max_letter:
		max_letter = ord(i)
	if ord(i)  < min_letter:
		min_letter = ord(i)


if k > n:
	result = result + s
	for i in range(k-n):
		result = result + chr(min_letter)
else:
	for i in xrange(k-1,-1,-1):
		if ord(s[i]) !=  max_letter:
			for j in xrange(ord(s[i])-96,26,1):
				if lex[j] == 1:
					result = result + chr(j+97)
					break
			result = s[:i]+result[::-1]
			break	
		else:
			result = result + chr(min_letter)
print result
