<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:
        part1 = set()
        part2 = set()
        n=len(nums)//2
        nums1 = nums[:n]
        nums2 = nums[n:]
        def part(val1, val2, i):
            if i==len(nums1):
                part1.add(val1)
            if i==len(nums2):
                part2.add(val2)
                return
            if i==len(nums1):
                case1 = part(val1, val2+nums2[i], i+1)
            else:
                case1 = part(val1+nums1[i], val2+nums2[i], i+1)
            case2 = part(val1, val2, i+1)
        part(0,0,0)
        res=math.inf
        part2=sorted(part2)
        for v in part1:
            l=bisect.bisect_left(part2, goal-v)
            res=min(res, abs(goal-(part2[l-1]+v)))
            if l<len(part2):
                res=min(res, abs(goal-(part2[l]+v)))
            if l+1<len(part2):
                res=min(res, abs(goal-(part2[l+1]+v)))
        return res
161000