Phone Numbers

给定 $n$，$k$ 和仅包含小写字母的字符串 $s$，请输出字典序最小的字符串 $t$，满足： - $|t| = k$。 - $t$ 的字典序比 $s$ 大。 - $t$ 中的任意一种字符都必须在 $s$ 中出现。

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 $ p_{i}<q_{i} $ and for all $ j<i $ it is satisfied that $ p_{j}=q_{j} $ . 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.

The first line of input contains two space separated integers $ n $ and $ k $ ( $ 1<=n,k<=100000 $ ) — 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 the string $ t $ conforming to the requirements above. It's guaranteed that the answer exists.

3 3
abc

aca

3 2
abc

ac

3 3
ayy

yaa

2 3
ba

baa

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.