<p>You are given a <strong>0-indexed</strong> integer array <code>nums</code> of length <code>n</code> and an integer <code>k</code>. In an operation, you can choose an element and multiply it by <code>2</code>.</p>

<p>Return <em>the maximum possible value of </em><code>nums[0] | nums[1] | ... | nums[n - 1]</code> <em>that can be obtained after applying the operation on nums at most </em><code>k</code><em> times</em>.</p>

<p>Note that <code>a | b</code> denotes the <strong>bitwise or</strong> between two integers <code>a</code> and <code>b</code>.</p>

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

<pre>
<strong>Input:</strong> nums = [12,9], k = 1
<strong>Output:</strong> 30
<strong>Explanation:</strong> If we apply the operation to index 1, our new array nums will be equal to [12,18]. Thus, we return the bitwise or of 12 and 18, which is 30.
</pre>

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

<pre>
<strong>Input:</strong> nums = [8,1,2], k = 2
<strong>Output:</strong> 35
<strong>Explanation:</strong> If we apply the operation twice on index 0, we yield a new array of [32,1,2]. Thus, we return 32|1|2 = 35.
</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;= 15</code></li>
</ul>

class Solution:
    def maximumOr(self, nums: List[int], k: int) -> int:
        num = max(nums)
        bit_counts = []
        while num > 0:
            bit_counts.append(0)
            num //= 2
        for num in nums:
            cur_bit = 0
            temp = num
            while temp > 0:
                bit_counts[cur_bit] += temp % 2
                temp //= 2
                cur_bit += 1
        result = 0
        for num in nums:
            if num < 2 ** (len(bit_counts)-1):
                continue
            my_bit_counts = [0] * len(bit_counts)
            temp = num
            cur_bit = 0
            while temp > 0:
                my_bit_counts[cur_bit] += temp % 2
                temp //= 2
                cur_bit += 1
            option = 0
            #print("procing {}".format(num))
            #print(bit_counts)
            #print(my_bit_counts)
            for i in range(0, len(bit_counts)):
                if bit_counts[i] > my_bit_counts[i]:
                    option = option | 2**i
                if my_bit_counts[i] > 0:
                    option = option | 2**(k+i)
            print(option)
            if option > result:
                result = option
        return result
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