<p>You are given a <strong>0-indexed</strong> positive integer array <code>nums</code> and a positive integer <code>k</code>.</p>
<p>A pair of numbers <code>(num1, num2)</code> is called <strong>excellent</strong> if the following conditions are satisfied:</p>
<ul>
<li><strong>Both</strong> the numbers <code>num1</code> and <code>num2</code> exist in the array <code>nums</code>.</li>
<li>The sum of the number of set bits in <code>num1 OR num2</code> and <code>num1 AND num2</code> is greater than or equal to <code>k</code>, where <code>OR</code> is the bitwise <strong>OR</strong> operation and <code>AND</code> is the bitwise <strong>AND</strong> operation.</li>
</ul>
<p>Return <em>the number of <strong>distinct</strong> excellent pairs</em>.</p>
<p>Two pairs <code>(a, b)</code> and <code>(c, d)</code> are considered distinct if either <code>a != c</code> or <code>b != d</code>. For example, <code>(1, 2)</code> and <code>(2, 1)</code> are distinct.</p>
<p><strong>Note</strong> that a pair <code>(num1, num2)</code> such that <code>num1 == num2</code> can also be excellent if you have at least <strong>one</strong> occurrence of <code>num1</code> in the array.</p>
