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  1. Prepare
  2. Algorithms
  3. Strings
  4. Find Strings

Find Strings

A substring is defined as a contiguous sequence of one or more characters in the string. More information on substrings can be found here.

You are given n strings w[1], w[2], ......, w[n]. Let S[i] denote the set of all distinct substrings of the string w[i]. Let , that is, S is a set of strings that is the union of all substrings in all sets S[1], S[2], ..... S[n]. There will be many queries. For each query you will be given an integer 'k'. Your task is to find the kth element of the -indexed lexicographically ordered set of substrings in the set S. If there is no element , return INVALID.

For example, your strings are . All of the substrings are and . Combine the two sets and sort them to get . So, for instance if , we return 'a'. If , we return 'bc'. If though, there is not an so we return INVALID.

Function Description

Complete the findStrings function in the editor below. It should return array of strings.

findStrings has the following parameter(s):

  • w: an array of strings
  • queries: an array of integers

Input Format

The first line contains an integer n, the number of strings in the array .
Each of the next n lines consists of a string .
The next line contains an integer q, the number of queries.
Each of the next q lines consists of a single integer k.

Constraints





Each character of

Output Format

Return an array of q strings where the ith string is the answer to the ith query. If a is invalid, return "INVALID" for that case.

Sample Input

2
aab
aac
3
3
8
23

Sample Output

aab
c
INVALID

Explanation

For the sample test case, we have 2 strings "aab" and "aac".
S1 = {"a", "aa", "aab", "ab", "b"} . These are the 5 unique substrings of "aab".
S2 = {"a", "aa", "aac",  "ac", "c" } . These are the 5 unique substrings of "aac".
Now, S = {S1 U S2} = {"a", "aa", "aab", "aac", "ab", "ac", "b", "c"}. Totally, 8 unique strings are present in the set S.
The lexicographically 3rd smallest string in S is "aab" and the lexicographically 8th smallest string in S is "c". Since there are only 8 distinct substrings, the answer to the last query is "INVALID".