CF940C.Phone Numbers

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.

电话号码在哪里？

给定一个由小写英文字母组成的字符串 $s$ 和一个整数 $k$。请找出长度为 $k$ 的字典序最小的字符串 $t$，使得 $t$ 中所含字母的集合是 $s$ 中所含字母的集合的子集，且 $s$ 的字典序严格小于 $t$。

保证答案一定存在。

注意：此处“字母的集合”指的是集合（set），而非多重集（multiset）。例如，字符串 abadaba 的字母集合为 $\{a,\,b,\,d\}$。

字符串 $p$ 的字典序小于字符串 $q$，当且仅当以下条件之一成立：

• $p$ 是 $q$ 的真前缀（即 $p$ 是 $q$ 的前缀且 $p \ne q$）；
• 或存在某个下标 $i$，使得 $p_i < q_i$，且对所有 $j < i$ 均有 $p_j = q_j$。

例如：abc 的字典序小于 abcd；abd 的字典序小于 abec；afa 的字典序不小于 ab；a 的字典序不小于 a。

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.

输入的第一行包含两个以空格分隔的整数 $n$ 和 $k$（$1 ≤ n, k ≤ 100\,000$）——分别表示字符串 $s$ 的长度以及字符串 $t$ 所需的长度。

输入的第二行包含字符串 $s$，它由 $n$ 个小写英文字母组成。

Output the string t conforming to the requirements above.

It's guaranteed that the answer exists.

输出符合上述要求的字符串 $t$。

保证答案存在。

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.

在第一个例子中，长度为 3 的字符串列表 $t$（其字母集合是 $s$ 的字母集合的子集）如下：aaa、aab、aac、aba、abb、abc、aca、acb、……。其中，字典序大于 abc 的字符串有：aca、acb、……。在这些字符串中，字典序最小的是 aca。