<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:
    @staticmethod
    def allSums(nums):
        n = len(nums)
        ans = []
        # for mask in range(1<<n):
        #     s = sum(((mask & (1<<j))>>j)*nums[j] for j in range(n))
        #     ans.append(s)
        for r in range(n+1):
            for c in combinations(nums, r):
                ans.append(sum( c))
        return ans
    @staticmethod
    def minAbsDifference(nums: List[int], goal: int) -> int:
        n = len(nums)
        sums_1 = Solution.allSums(nums[:n//2])
        sums_2 = sorted(Solution.allSums(nums[n//2:]))
        ans = abs(goal)
        for s1 in sums_1:
            i2 = bisect.bisect(sums_2, goal-s1)
            if i2 < len(sums_2): ans = min(ans, abs(goal-s1-sums_2[i2]))
            if i2 > 0: ans = min(ans, abs(goal-s1-sums_2[i2-1]))
        return ans
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