You are given an integer array <code>nums</code> and a <strong>positive</strong> integer <code>k</code>.
<p>A <span data-keyword="subsequence-array">subsequence</span> <code>sub</code> of <code>nums</code> with length <code>x</code> is called <strong>valid</strong> if it satisfies:</p>

<ul>
	<li><code>(sub[0] + sub[1]) % k == (sub[1] + sub[2]) % k == ... == (sub[x - 2] + sub[x - 1]) % k.</code></li>
</ul>
Return the length of the <strong>longest</strong> <strong>valid</strong> subsequence of <code>nums</code>.
<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">nums = [1,2,3,4,5], k = 2</span></p>

<p><strong>Output:</strong> <span class="example-io">5</span></p>

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

<p>The longest valid subsequence is <code>[1, 2, 3, 4, 5]</code>.</p>
</div>

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

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">nums = [1,4,2,3,1,4], k = 3</span></p>

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

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

<p>The longest valid subsequence is <code>[1, 4, 1, 4]</code>.</p>
</div>

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

<ul>
	<li><code>2 &lt;= nums.length &lt;= 10<sup>3</sup></code></li>
	<li><code>1 &lt;= nums[i] &lt;= 10<sup>7</sup></code></li>
	<li><code>1 &lt;= k &lt;= 10<sup>3</sup></code></li>
</ul>