B"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, xe2 x80 x89b, xe2 x80 x89d}. 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 xe2 x80 x89< xe2 x80 x89qi and for all j xe2 x80 x89< xe2 x80 x89i it is satisfied that pj xe2 x80 x89= xe2 x80 x89qj. 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 xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89n, xe2 x80 x89k xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89100 xe2 x80 x89000) -- 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. 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. "...