<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>

from decimal import Decimal

    

class Solution:
    def splitArraySameAverage(self, nums: List[int]) -> bool:
        
        if not nums:
            return target == 0
        self.nums = nums
        
        total = sum(nums)
        avg_ = Decimal(total) / Decimal(len(nums))
        
        for i in range(1, len(nums)//2+1):
            
            if floor(avg_ * i) != avg_ * i:
                continue
            # print(avg_)
            # print(i)
            # print(avg_ * i)
            if self.knapsack(avg_ * i, len(nums)-1, i):
                return True
        return False
        
    @cache
    def knapsack(self, target, idx, remaining):
        # if target == 0:
        #     return remaining == 0
        if remaining == 0:
            return target == 0
        if target == 0 and remaining == 0:
            return True
        if idx == -1:
            return False
        
        return self.knapsack(target - self.nums[idx], idx-1, remaining -1) or self.knapsack(target, idx-1, remaining)
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