<p>You are given an integer array <code>nums</code> and an integer <code>goal</code>.</p>

<p>You want to choose a subsequence of <code>nums</code> such that the sum of its elements is the closest possible to <code>goal</code>. That is, if the sum of the subsequence&#39;s elements is <code>sum</code>, then you want to <strong>minimize the absolute difference</strong> <code>abs(sum - goal)</code>.</p>

<p>Return <em>the <strong>minimum</strong> possible value of</em> <code>abs(sum - goal)</code>.</p>

<p>Note that a subsequence of an array is an array formed by removing some elements <strong>(possibly all or none)</strong> of the original array.</p>

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

<pre>
<strong>Input:</strong> nums = [5,-7,3,5], goal = 6
<strong>Output:</strong> 0
<strong>Explanation:</strong> Choose the whole array as a subsequence, with a sum of 6.
This is equal to the goal, so the absolute difference is 0.
</pre>

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

<pre>
<strong>Input:</strong> nums = [7,-9,15,-2], goal = -5
<strong>Output:</strong> 1
<strong>Explanation:</strong> Choose the subsequence [7,-9,-2], with a sum of -4.
The absolute difference is abs(-4 - (-5)) = abs(1) = 1, which is the minimum.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> nums = [1,2,3], goal = -7
<strong>Output:</strong> 7
</pre>

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

<ul>
	<li><code>1 &lt;= nums.length &lt;= 40</code></li>
	<li><code>-10<sup>7</sup> &lt;= nums[i] &lt;= 10<sup>7</sup></code></li>
	<li><code>-10<sup>9</sup> &lt;= goal &lt;= 10<sup>9</sup></code></li>
</ul>

class Solution:
    def minAbsDifference(self, nums: List[int], goal: int) -> int:
        if len(nums) == 1:
            return min(abs(goal), abs(nums[0] - goal))

        n = len(nums) // 2
        m = len(nums) - n


        # Right: 2^m combination
        
        def get_subset(arr):
            ret = []
            for i in range(1 << len(arr)): #0 ~ 2^m
                sum  = 0
                for j in range(len(arr)):
                    if ((1 << j) & i):
                        sum += arr[j]
                ret.append(sum)
            return ret
        
        one = get_subset(nums[:n])
        two = get_subset(nums[n:])
        two.sort()

        # Left: 2^n combination. 
        min_val = float('infinity')
        for left in one:
            idx = bisect_left(two, goal - left)
            if idx < len(two):
                min_val = min(min_val, abs(two[idx] + left - goal))
            if idx > 0:
                min_val = min(min_val, abs(two[idx - 1] + left - goal))

        return min_val
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