1968: Dense Subsequence
Description
You are given a string s, consisting of lowercase English letters, and the integer m.
One should choose some symbols from the given string so that any contiguous subsegment of length m has at least one selected symbol. Note that here we choose positions of symbols, not the symbols themselves.
Then one uses the chosen symbols to form a new string. All symbols from the chosen position should be used, but we are allowed to rearrange them in any order.
Formally, we choose a subsequence of indices 1≤i1<i2<...<it≤|s|. The selected sequence must meet the following condition: for every j such that 1≤j≤|s|-m+1, there must be at least one selected index that belongs to the segment [j,j+m-1], i.e. there should exist a k from 1 to t, such that j≤ik≤j+m-1.
Then we take any permutation p of the selected indices and form a new string sip1sip2... sipt.
Find the lexicographically smallest string, that can be obtained using this procedure.
The first line of the input contains a single integer m (1≤m≤100000).
The second line contains the string s consisting of lowercase English letters. It is guaranteed that this string is non-empty and its length doesn't exceed 100000. It is also guaranteed that the number m doesn't exceed the length of the string s.
Print the single line containing the lexicographically smallest string, that can be obtained using the procedure described above.
3
cbabc
a
2
abcab
aab
3
bcabcbaccba
aaabb
In the first sample, one can choose the subsequence {3} and form a string "a".
In the second sample, one can choose the subsequence {1,2,4} (symbols on this positions are 'a', 'b' and 'a') and rearrange the chosen symbols to form a string "aab".