Solve the programming task below in a Python markdown code block.
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You are given an integer $n$ and a string $s$ consisting only of characters 'a' and 'b'. Consider a string $t = \underbrace{s + s + \dots + s}_{n\text{ times}}$, i.e. the string obtained by concatenating $n$ copies of $s$.

Find the number of non-empty prefixes of $t$ in which the number of occurrences of 'a' is strictly greater than the number of occurrences of 'b'.

------  Input ------
The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.
The first and only line of each test case contains the string $s$ and the integer $n$, separated by a single space. 

------  Output ------
For each test case, print a single line containing one integer — the number of valid prefixes.

------  Constraints  ------
$1 ≤ T ≤ 100$
$1 ≤ |s| ≤ 10^{3}$
$1 ≤ n ≤ 10^{9}$
each character of $s$ is either 'a' or 'b'

------  Subtasks ------
Subtask #1 (30 points): $1 ≤ n ≤ 10^{3}$

Subtask #2 (70 points): original constraints

----- Sample Input 1 ------ 
3
aba 2
baa 3
bba 3
----- Sample Output 1 ------ 
5
6
0
----- explanation 1 ------ 
Example case 1: The string $t$ is "abaaba". It has five prefixes which contain more a-s than b-s: "a", "aba", "abaa", "abaab" and "abaaba".

Example case 2: The string $t$ is "baabaabaa". The strings "baa", "baaba", "baabaa", "baabaab", "baabaaba" and "baabaabaa" are the six valid prefixes.

Example case 3: The string $t$ is "bbabbabba". There is no prefix of this string which consists of more a-s than b-s. Therefore, the answer is zero.