<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 is_sum_exist(self, idx: int, count: int, remain: int):
        if count == 0 and remain == 0:
            return True
        
        if count < 0:
            return False
        
        if remain < 0:
            return False
        
        if idx >= len(self.nums):
            return False
        
        if remain > self.nums[idx] * count:
            return False
        
        delta = 1
        for i in range(idx + 1, len(self.nums)):
            if self.nums[i] != self.nums[idx]:
                break
                
            delta += 1
            
        return any(
            self.is_sum_exist(idx + delta, count - d, remain - self.nums[idx] * d)
            for d in range(0, delta + 1)
        )
    
    def splitArraySameAverage(self, nums: List[int]) -> bool:
        # partial = choose from nums
        # sum(partial) / len(partial) == (sum(nums) - sum(partial)) / (len(nums) - len(partial))
        # sum(partial) * len(nums) == sum(nums) * len(partial)
        # sum(partial) / len(partial) == sum(nums) / len(nums)
        self.nums = nums
        self.nums.sort(reverse=True)
        
        num_sum = sum(nums)
        for count in range(1, len(nums) // 2 + 1):
            d, r = divmod(num_sum * count, len(nums))
            if r != 0:
                continue
                
            if self.is_sum_exist(0, count, d):
                return True
            
        return False

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