<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>

import bisect

class Solution:
    def minAbsDifference(self, nums: List[int], goal: int) -> int:
        
        # def dfs(arr: list, i: int, total: int, log: set) -> None:
        #     if i == len(arr):
        #         log.add(total)
        #         return
            
        #     dfs(arr, i + 1, total, log)
        #     dfs(arr, i + 1, total + arr[i], log)
        
        # sum1, sum2 = set(), set()

        # dfs(nums[:len(nums) // 2], 0, 0, sum1)
        # dfs(nums[len(nums) // 2:], 0, 0, sum2)

        def sums(arr):
            sums = {0}
            for a in arr:
                sums |= {s + a for s in sums}
            return sums        
        sum1 = sums(nums[1::2])
        s2 = sorted(sums(nums[::2]))

        ans = float('inf')

        for s in sum1:
            diff = goal - s
            idx = bisect_left(s2, diff)

            if idx < len(s2):
                ans = min(ans, abs(diff - s2[idx]))
            if idx > 0:
                ans = min(ans, abs(diff - s2[idx - 1]))
        
        return ans
35800