<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>

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

<pre>
<strong>Input:</strong> nums = [1,2,3,1], k = 3
<strong>Output:</strong> 5
<strong>Explanation:</strong> The excellent pairs are the following:
- (3, 3). (3 AND 3) and (3 OR 3) are both equal to (11) in binary. The total number of set bits is 2 + 2 = 4, which is greater than or equal to k = 3.
- (2, 3) and (3, 2). (2 AND 3) is equal to (10) in binary, and (2 OR 3) is equal to (11) in binary. The total number of set bits is 1 + 2 = 3.
- (1, 3) and (3, 1). (1 AND 3) is equal to (01) in binary, and (1 OR 3) is equal to (11) in binary. The total number of set bits is 1 + 2 = 3.
So the number of excellent pairs is 5.</pre>

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

<pre>
<strong>Input:</strong> nums = [5,1,1], k = 10
<strong>Output:</strong> 0
<strong>Explanation:</strong> There are no excellent pairs for this array.
</pre>

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

<ul>
	<li><code>1 &lt;= nums.length &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= nums[i] &lt;= 10<sup>9</sup></code></li>
	<li><code>1 &lt;= k &lt;= 60</code></li>
</ul>

class Solution:
    def countExcellentPairs(self, nums: List[int], k: int) -> int:
        # set bits 1 and set bits 2, 
        # For or operation, set bits 1 + set bits 2 - set bits both have
        # For and operation, set bits both have
        # if we want the sum of both operations, we get set bits 1 + set bits 2
        # and this value should be greater than or equal to k

        # Step 1, we need to find each number's number of set bits and record it in to an array that has length 0 to 32 indicate the bits count.
        # Step 2, we just make suffix sum with that array, so we can know how many numbers that is big enough for some number
        # 0  1   2  3   4    5
        # [0 0   1  1   2    1 ]
        # [5 5   5  4   3    1 ]
        # we want to see how many pairs with 0, k is 3
        # so we can just do ary[3] to know there is 4 numbers are >= 3
        # pairs should be 8

        set_bits_count = [0] * 33
        counts = []
        excellent_pairs = 0

        for num in list(set(nums)):
            count = Counter(format(num, 'b'))["1"]
            counts.append(count)
            set_bits_count[count] += 1

        for i in range(31, -1, -1):
            set_bits_count[i] += set_bits_count[i+1]

        # print(set_bits_count)
        # print(counts)

        for count in counts:
            need = max(0, k - count)
            if need > 32:
                continue
            excellent_pairs += set_bits_count[need]

        return excellent_pairs
34900