<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>

from sortedcontainers import SortedSet

class Solution:
    def minAbsDifference(self, nums: List[int], goal: int) -> int:
        n = len(nums)
        p1, p2 = nums[:n // 2], nums[n//2:]
        cur = inc = 0
        res1, res2 = SortedSet(), SortedSet()

        def bt(i, arr, res):
            nonlocal cur, inc
            if i == len(arr):
                if inc:
                    res.add(cur)
                return
            cur += arr[i]
            inc += 1
            bt(i + 1, arr, res)
            cur -= arr[i]
            inc -= 1
            bt(i + 1, arr, res)
        bt(0, p1, res1)
        bt(0, p2, res2)
        res = abs(goal)
        for num in res1:
            res = min(res, abs(num - goal))
            j = res2.bisect_left(goal - num)
            if j != len(res2):
                res = min(res, abs(goal - num - res2[j]))
            if j != 0:
                res = min(res, abs(goal - num - res2[j - 1]))
        for num in res2:
            res = min(res, abs(num - goal))
        return res
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