github.com/captn3m0/codechef.git

---
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---
<span class="solution-visible-txt">All submissions for this problem are available.</span><h3> Read problems statements in <a target="_blank" href="http://www.codechef.com/download/translated/COOK81/mandarin/ABREPEAT.pdf">Mandarin Chinese</a>, <a target="_blank" href="http://www.codechef.com/download/translated/COOK81/russian/ABREPEAT.pdf">Russian</a> and <a target="_blank" href="http://www.codechef.com/download/translated/COOK81/vietnamese/ABREPEAT.pdf">Vietnamese</a> as well.</h3>


<p>Limak has a string <b>S</b>, that consists of <b>N</b> lowercase English letters.
Limak then created a new string by repeating <b>S</b> exactly <b>K</b> times.
For example, for <b>S</b> = "abcb" and <b>K</b> = 2, he would get "abcbabcb".</p>

<p>Your task is to count the number of subsequences "ab" (not necessarily consecutive) in the new string.</p>

<p>In other words, find the number pairs of indices i < j, such that the i-th and j-th characters in the new string are 'a' and 'b' respectively.</p>



<h3>Input</h3>

<p>The first line of the input contains an integer <b>T</b> denoting the number of test cases. The description of <b>T</b> test cases follows.</p>

<p>The first line of each test case contains two integers <b>N</b> and <b>K</b>, denoting the length of the initial string <b>S</b> and the number of repetitions respectively.</p>

<p>The second line contains a string <b>S</b>.
Its length is exactly <b>N</b>, and each of its characters is a lowercase English letter.</p>



<h3>Output</h3>

<p>For each test case, output a single line containing one integer — the number of subsequences "ab" in the new string.
For the given constraints, it can be proved that the answer fits in the 64-bit signed type.</p>



<h3>Constraints</h3>

<ul>
<li>1 ≤ <b>T</b> ≤ 10</li>
<li>1 ≤ <b>N</b> ≤ 10<sup>5</sup></li>
<li>1 ≤ <b>N</b> * <b>K</b> ≤ 10<sup>9</sup> (in other words, the new string has length up to 10<sup>9</sup>)</li>
</ul>


<h3>Example</h3>

<pre><b>Input:</b>
3
4 2
abcb
7 1
aayzbaa
12 80123123
abzbabzbazab

<b>Output:</b>
6
2
64197148392731290
</pre>



<h3>Explanation</h3>

<p><b>Test case 1.</b> Limak repeated the string "abcb" 2 times, and so he got "abcbabcb". There are 6 occurrences of the subsequence "ab":</p>

<ul>
<li>ABcbabcb (the two letters marked uppercase)</li>
<li>AbcBabcb</li>
<li>AbcbaBcb</li>
<li>AbcbabcB</li>
<li>abcbABcb</li>
<li>abcbAbcB</li>
</ul>

<p><b>Test case 2.</b> Since <b>K</b> = 1, the new string is equal to the given <b>S</b> ("aayzbaa"). There are 2 occurrences of the subsequence "ab" in this string: AayzBaa and aAyzBaa.</p>