You are given a string S consisting of lowercase alphabets and an integer array val consisting of N integers. Using the given string S and array val, you need to create another string X according to the code snippet below:

Initially string X is empty
Let len be the length of string S

for i := 0 to N-1
    pos := absolute value of val[i]
    if(val[i] >= 0)
      X := X + S[0,pos] // append substring of string S from index 0 to pos (both including) into X
    else
      X := X + S[pos,len-1] // append substring of string S from index pos to len-1 (both including) into X

You have to answer Q tasks. For each task, you are given an integer K and you have to print the K^th vowel in the string X. If the K^th vowel doesn't exist print -1.

Note: The vowels are a, e, i, o, and u.

Input Format:

The first line contains a string S.

The second line contains an integer N.

The third line contains N space-separated integers, denoting the element of the array val.

The fourth line contains an integer Q, denoting the number of tasks.

The fifth line contains Q space-separated integers, denoting the tasks.

Output Format:

Print the answer for each of the Q tasks in a newline.

Constraints:

\(1 \le |S|,N,Q \le10^5\)

\(0\le |val_i| \le|S|-1\)

\(1 \le K \le 10^{10}\)

All the characters of string S are lowercase characters only.