Little Daniel loves to play with strings! He always finds different ways to have fun with strings! Knowing that, his friend Kinan decided to test his skills so he gave him a string S and asked him Q questions of the form:
If all distinct substrings of string S were sorted lexicographically, which one will be the K-th smallest?
After knowing the huge number of questions Kinan will ask, Daniel figured out that he can’t do this alone. Daniel, of course, knows your exceptional programming skills, so he asked you to write him a program which given S will answer Kinan’s questions.

Example:
S = “aaa” (without quotes)
substrings of S are “a” , “a” , “a” , “aa” , “aa” , “aaa”. The sorted list of substrings will be:
“a”, “aa”, “aaa”.

Input

In the first line there is Kinan’s string S (with length no more than 90000 characters). It contains only small letters of English alphabet. The second line contains a single integer Q (Q <= 500) , the number of questions Daniel will be asked. In the next Q lines a single integer K is given (0 < K < 2^31).

Output

Output consists of Q lines, the i-th contains a string which is the answer to the i-th asked question.

Example

Input:
aaa
2
2
3

Output:

aa
aaa

题解

lazycal：

给一个长度不超过90000的串S，每次询问它的所有不同子串中，字典序第K小的，询问不超过500个。

搞出后缀自动机

dp处理出每个点往下走能够走出多少个串。
f[i]=sigma(f[ch[i][c])+1
这个可以按Max排序之后倒着推就好了。
询问的时候看一下走下去个数是否<=k，是的话就走下去，然后–k；否则就找下一条边。