<p>You are playing a game involving a <strong>circular</strong> array of non-zero integers <code>nums</code>. Each <code>nums[i]</code> denotes the number of indices forward/backward you must move if you are located at index <code>i</code>:</p>

<ul>
	<li>If <code>nums[i]</code> is positive, move <code>nums[i]</code> steps <strong>forward</strong>, and</li>
	<li>If <code>nums[i]</code> is negative, move <code>nums[i]</code> steps <strong>backward</strong>.</li>
</ul>

<p>Since the array is <strong>circular</strong>, you may assume that moving forward from the last element puts you on the first element, and moving backwards from the first element puts you on the last element.</p>

<p>A <strong>cycle</strong> in the array consists of a sequence of indices <code>seq</code> of length <code>k</code> where:</p>

<ul>
	<li>Following the movement rules above results in the repeating index sequence <code>seq[0] -&gt; seq[1] -&gt; ... -&gt; seq[k - 1] -&gt; seq[0] -&gt; ...</code></li>
	<li>Every <code>nums[seq[j]]</code> is either <strong>all positive</strong> or <strong>all negative</strong>.</li>
	<li><code>k &gt; 1</code></li>
</ul>

<p>Return <code>true</code><em> if there is a <strong>cycle</strong> in </em><code>nums</code><em>, or </em><code>false</code><em> otherwise</em>.</p>

<p>&nbsp;</p>
<p><strong>Example 1:</strong></p>

<pre>
<strong>Input:</strong> nums = [2,-1,1,2,2]
<strong>Output:</strong> true
<strong>Explanation:</strong>
There is a cycle from index 0 -&gt; 2 -&gt; 3 -&gt; 0 -&gt; ...
The cycle&#39;s length is 3.
</pre>

<p><strong>Example 2:</strong></p>

<pre>
<strong>Input:</strong> nums = [-1,2]
<strong>Output:</strong> false
<strong>Explanation:</strong>
The sequence from index 1 -&gt; 1 -&gt; 1 -&gt; ... is not a cycle because the sequence&#39;s length is 1.
By definition the sequence&#39;s length must be strictly greater than 1 to be a cycle.
</pre>

<p><strong>Example 3:</strong></p>

<pre>
<strong>Input:</strong> nums = [-2,1,-1,-2,-2]
<strong>Output:</strong> false
<strong>Explanation:</strong>
The sequence from index 1 -&gt; 2 -&gt; 1 -&gt; ... is not a cycle because nums[1] is positive, but nums[2] is negative.
Every nums[seq[j]] must be either all positive or all negative.
</pre>

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

<ul>
	<li><code>1 &lt;= nums.length &lt;= 5000</code></li>
	<li><code>-1000 &lt;= nums[i] &lt;= 1000</code></li>
	<li><code>nums[i] != 0</code></li>
</ul>

<p>&nbsp;</p>
<p><strong>Follow up:</strong> Could you solve it in <code>O(n)</code> time complexity and <code>O(1)</code> extra space complexity?</p>