<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:
        mid = len(nums) // 2
        subSum1 = self.__getSubsequences(nums[:mid], 0, 0)
        subSum2 = self.__getSubsequences(nums[mid:], 0, 0)
        subSum2.sort()
        ans = sys.maxsize
        for ss in subSum1:
            counterPart = goal - ss
            idx = self.__binarySearchLeft(subSum2, counterPart)
            if idx < len(subSum2):
                ans = min(ans, abs(counterPart-subSum2[idx]))
            if idx > 0:
                ans = min(ans, abs(counterPart-subSum2[idx-1]))
        return ans

    
    def __getSubsequences(self, nums, i, subSum):
        if i == len(nums):
            return [subSum]
        current = nums[i]
        taken = self.__getSubsequences(nums, i+1, subSum+current)
        ignored = self.__getSubsequences(nums, i+1, subSum)
        return taken + ignored

    def __binarySearchLeft(self, nums, target):
        s, e = 0, len(nums)-1
        ans = -1
        while s <= e:
            m = s + ((e-s)//2)
            if nums[m] >= target:
                ans = m
                e = m-1
            else:
                s = m+1
        return ans
112400