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.
def small(s):
    small='z'
    for i in range(n):
        if s[i]<small:
            small=s[i]
    return small
import sys    
n,k=map(int,sys.stdin.readline().split())
s=input()
if k>n:
    ans=""
    ans+=s
    sm=small(s)
    for i in range(k-n):
        ans+=sm
    print(ans)
else:
    ans=list(s[:k])
    arr=[0]*26 
    for i in range(n):
        arr[ord(s[i])-97]+=1
    sm=small(s)
    flag=False
    for i in range(k-1,-1,-1):
        for j in range(26):
            if arr[j]>0 and ord(ans[i])-97<j:
                ans[i]=chr(j+97)
                flag=True
                break
        if flag:
            break
        else:
            ans[i]=sm
    print(''.join(ans))            
     
        
            
        
