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.
# -*- coding: utf-8 -*-

n, k = map(int,raw_input().split())
st = raw_input()
mark = [ord(s) for s in st]
maxm = max(mark)
#print(chr(maxm))
ns=''
if k>n:
    ns = st+chr(min(mark))*(k-n)
elif maxm == mark[min(k-1,len(mark)-1)]:    
    lel = mark[min(k-1,len(mark)-1)]
    for i in range(k-1,-1,-1):
        #print(mark[i],maxm)
        if(mark[i]<maxm):
            if k>i+1:
                mmin=maxm
                for m in mark:
                    if m<mmin and m>mark[i]: mmin=m
                #print(1,chr(mark[i]),chr(maxm),)
                ns = st[:i]+chr(mmin)
                ns += chr(min(mark))*(k-len(ns))
            else:
                mmin=maxm
                for m in mark:
                    if m<mmin and m>mark[k-1]: mmin=m
                #print(chr(mark[k-1]),chr(maxm))                        
                ns = st[:k-1]+chr(mmin)
            break

else:
    mmin=maxm
    for m in mark:
        if m<mmin and m>mark[min(k-1,len(mark)-1)]: mmin=m
    ns = st[:min(k-1,len(mark)-1)]+chr(mmin)
    
print(ns)