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.
x=input().split()
x=[int(i) for i in x]
#print(x[0]+1)
z=input()
max='a'
for i in z:
	if(max<i):
		max=i
min='z'
for i in z:
	if(min>i):
		min=i
b=-1

if(x[0]<x[1]):
	km=x[0]
else:
	km=x[1]
for i in range(km-1,-1,-1):
	if(z[i]!=max):
		b=i
		break
l='z'
for i in z:
	if i>z[b] and i<l:
		l=i
#print(x[1],x[0])
if(x[1]>x[0]):
	#print("hi")
	print(z+(x[1]-x[0])*min)
else:
	print(z[:b]+l+(x[1]-b-1)*min)



