Count Good Prefixes

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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 nonempty 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  $1 \le T \le 100$  $1 \le s \le 10^3$  $1 \le n \le 10^9$  each character of $s$ is either 'a' or 'b' ### Subtasks **Subtask #1 (30 points):** $1 \le n \le 10^3$ **Subtask #2 (70 points):** original constraints ### Sample Input3 aba 2 baa 3 bba 3### Sample Output
5 6 0### Explanation **Example case 1:** The string $t$ is "abaaba". It has five prefixes which contain more as than bs: "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 as than bs. Therefore, the answer is zero.
Author:  admin2 
Editorial  https://discuss.codechef.com/problems/GOODPREF 
Tags  admin2, april18, logic, math, string 
Date Added:  2042018 
Time Limit:  1 sec 
Source Limit:  50000 Bytes 
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