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=input().split()
n,k=int(n),int(k)

s=list(input())
st=s[:k]

s.sort()

a=[s[0]]

b=True

for i in range(1,len(s)):
	if s[i]!=s[i-1]:
		a.append(s[i])

#print(st)
while len(st)<k:
	st.append(a[0])
	b=False


#print(a)
if b:
	for i in reversed(range(k)):
		if st[i]!=a[len(a)-1]:
			#print(st[i])
			for j in range(len(a)-1):
				if st[i]==a[j]:
					st[i]=a[j+1]
					break
			for j in range(i+1,k):
				st[j]=a[0]
			break

stri=''
for r in st:
	stri=stri+r
print(stri)