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/JUNE16/mandarin/CHEFARK.pdf">Mandarin Chinese</a>, <a target="_blank" href="http://www.codechef.com/download/translated/JUNE16/russian/CHEFARK.pdf">Russian</a> and <a target="_blank" href="http://www.codechef.com/download/translated/JUNE16/vietnamese/CHEFARK.pdf">Vietnamese</a> as well.</h3>


<p>Chef has an array <b>A</b> consisting of <b>N</b> integers. He also has an intger <b>K</b>.</p>

<p>Chef wants you to find out number of different arrays he can obtain from array <b>A</b> by applying the following operation <b>exactly</b> <b>K</b> times.
<ul>
<li>Pick some element in the array and multiply it by <b>-1</b></li>
</ul>
</p>

<p>
As answer could be quite large, print it modulo <b>10<sup>9</sup> + 7</b>.
</p>

<h3>Input</h3>
<ul>
<li>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.</li>
<li>The first line of each test case contains two space separated integers <b>N</b>, <b>K</b> as defined above.</li>
<li>The second line contains <b>N</b> space-separated integers <b>A<sub>1</sub></b>, <b>A<sub>2</sub></b>, ..., <b>A<sub>N</sub></b> denoting the elements of the array.</li>
</ul>

<h3>Output</h3>
<ul>
<li>For each test case, output a single line containing an integer corresponding to the number of different arrays Chef can get modulo <b>10<sup>9</sup> + 7</b>.</li>
</ul>

<h3>Constraints</h3>
<ul>
<li><b>1</b> ≤ <b>T</b> ≤ <b>10</b></li>
<li><b>1</b> ≤ <b>N, K</b> ≤ <b>10<sup>5</sup></b></li>
<li><b>-10<sup>6</sup></b> ≤ <b>A<sub>i</sub></b> ≤ <b>10<sup>6</sup></b></li>
</ul>

<h3>Subtasks</h3>
<ul>
<li><b>Subtask #1 (10 points)</b> : <b>N, K</b> ≤ <b>10</b></li>
<li><b>Subtask #2 (30 points)</b> : <b>N, K</b> ≤ <b>100</b></li>
<li><b>Subtask #3 (60 points)</b> : <b>N, K</b> ≤ <b>10<sup>5</sup></b></li>
</ul>

<h3>Example</h3>
<pre><b>Input:</b>
3
1 3
100
3 1
1 2 1
3 2
1 2 1

<b>Output:</b>
1
3
4
</pre>

<h3>Explanation</h3>
<p><b>Example case 1.</b>
Chef has only one element and must apply the operation 3 times to it. After applying the operations, he will end up with -100. That is the only array he will get.
</p>
<p><b>Example case 2.</b>
Chef can apply operation to one of three elements. So, he can obtain three different arrays.
</p>
<p><b>Example case 3.</b>
Note that other than applying operation to positions <b>(1, 2)</b>, <b>(1, 3)</b>, <b>(2, 3)</b>, Chef can also apply the operation twice on some element and get the original.
</p>
<p>In summary, Chef can get following four arrays.
<pre>
[1, 2, 1]
[-1, -2, 1]
[-1, 2, -1]
[1, -2, -1]
</pre>