<p>A <strong>powerful array</strong> for an integer <code>x</code> is the shortest sorted array of powers of two that sum up to <code>x</code>. For example, the powerful array for 11 is <code>[1, 2, 8]</code>.</p>

<p>The array <code>big_nums</code> is created by concatenating the <strong>powerful</strong> arrays for every positive integer <code>i</code> in ascending order: 1, 2, 3, and so forth. Thus, <code>big_nums</code> starts as <code>[<u>1</u>, <u>2</u>, <u>1, 2</u>, <u>4</u>, <u>1, 4</u>, <u>2, 4</u>, <u>1, 2, 4</u>, <u>8</u>, ...]</code>.</p>

<p>You are given a 2D integer matrix <code>queries</code>, where for <code>queries[i] = [from<sub>i</sub>, to<sub>i</sub>, mod<sub>i</sub>]</code> you should calculate <code>(big_nums[from<sub>i</sub>] * big_nums[from<sub>i</sub> + 1] * ... * big_nums[to<sub>i</sub>]) % mod<sub>i</sub></code><!-- notionvc: a71131cc-7b52-4786-9a4b-660d6d864f89 -->.</p>

<p>Return an integer array <code>answer</code> such that <code>answer[i]</code> is the answer to the <code>i<sup>th</sup></code> query.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">queries = [[1,3,7]]</span></p>

<p><strong>Output:</strong> <span class="example-io">[4]</span></p>

<p><strong>Explanation:</strong></p>

<p>There is one query.</p>

<p><code>big_nums[1..3] = [2,1,2]</code>. The product of them is 4. The remainder of 4 under 7 is 4.</p>
</div>

<p><strong class="example">Example 2:</strong></p>

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">queries = [[2,5,3],[7,7,4]]</span></p>

<p><strong>Output:</strong> <span class="example-io">[2,2]</span></p>

<p><strong>Explanation:</strong></p>

<p>There are two queries.</p>

<p>First query: <code>big_nums[2..5] = [1,2,4,1]</code>. The product of them is 8. The remainder of 8 under 3 is 2.</p>

<p>Second query: <code>big_nums[7] = 2</code>. The remainder of 2 under 4 is 2.</p>
</div>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= queries.length &lt;= 500</code></li>
	<li><code>queries[i].length == 3</code></li>
	<li><code>0 &lt;= queries[i][0] &lt;= queries[i][1] &lt;= 10<sup>15</sup></code></li>
	<li><code>1 &lt;= queries[i][2] &lt;= 10<sup>5</sup></code></li>
</ul>