Weighted Uniform Strings

A weighted string is a string of lowercase English letters where each letter has a weight. Character weights are to from to as shown below:

The weight of a string is the sum of the weights of its characters. For example:
A uniform string consists of a single character repeated zero or more times. For example, ccc and a are uniform strings, but bcb and cd are not.

Given a string, , let be the set of weights for all possible uniform contiguous substrings of string . There will be queries to answer where each query consists of a single integer. Create a return array where for each query, the value is Yes if . Otherwise, append No.

Note: The symbol denotes that is an element of set .

Example

.

Working from left to right, weights that exist are:

string  weight
a       1
b       2
bb      4
c       3
cc      6
ccc     9
d       4
dd      8
ddd     12
dddd    16

Now for each value in , see if it exists in the possible string weights. The return array is ['Yes', 'No', 'No', 'Yes', 'No'].

Function Description

Complete the weightedUniformStrings function in the editor below.

weightedUniformStrings has the following parameter(s):
- string s: a string
- int queries[n]: an array of integers

Returns
- string[n]: an array of strings that answer the queries

Input Format

The first line contains a string , the original string.
The second line contains an integer , the number of queries.
Each of the next lines contains an integer , the weight of a uniform subtring of that may or may not exist.

Constraints

will only contain lowercase English letters, ascii[a-z].

Sample Input 0

abccddde
6
1
3
12
5
9
10

Sample Output 0

Yes
Yes
Yes
Yes
No
No

Explanation 0

The weights of every possible uniform substring in the string abccddde are shown below:

We print Yes on the first four lines because the first four queries match weights of uniform substrings of . We print No for the last two queries because there are no uniform substrings in that have those weights.

Note that while de is a substring of that would have a weight of , it is not a uniform substring.

Note that we are only dealing with contiguous substrings. So ccc is not a substring of the string ccxxc.

Sample Input 1

aaabbbbcccddd
5
9
7
8
12
5

Sample Output 1

Yes
No
Yes
Yes
No