<p>You are given an integer array <code>nums</code>.</p>

<p>You should move each element of <code>nums</code> into one of the two arrays <code>A</code> and <code>B</code> such that <code>A</code> and <code>B</code> are non-empty, and <code>average(A) == average(B)</code>.</p>

<p>Return <code>true</code> if it is possible to achieve that and <code>false</code> otherwise.</p>

<p><strong>Note</strong> that for an array <code>arr</code>, <code>average(arr)</code> is the sum of all the elements of <code>arr</code> over the length of <code>arr</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> nums = [1,2,3,4,5,6,7,8]
<strong>Output:</strong> true
<strong>Explanation:</strong> We can split the array into [1,4,5,8] and [2,3,6,7], and both of them have an average of 4.5.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> nums = [3,1]
<strong>Output:</strong> false
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= nums.length &lt;= 30</code></li>
	<li><code>0 &lt;= nums[i] &lt;= 10<sup>4</sup></code></li>
</ul>


class Solution:
    def splitArraySameAverage(self, nums):
        n, total = len(nums), sum(nums)

        @lru_cache(None)
        def function(i,target,k):
            if k == 0:
                return target == 0

            if k+i > n:
                return False 

            return function(i+1,target-nums[i],k-1) or function(i+1,target,k)

        for j in range(1,n//2+1):
            if function(0,total*j//n,j) and total*j%n == 0:
                return True 

        return False 
        
        def possible_sums(arr: List[int]) -> int:
            subset_sums = 1
            for a in arr:
                subset_sums |= (subset_sums << a)
            return (subset_sums - 1) ^ (1 << sum(arr))
        
        transformed_nums = [n * num - total_sum for num in nums]
        
        if 0 in transformed_nums:
            return True
        
        positives = [num for num in transformed_nums if num > 0]
        negatives = [-num for num in transformed_nums if num < 0]
        
        return bool(possible_sums(positives) & possible_sums(negatives))
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