<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: List[int]) -> bool:
        if len(nums) == 1:return False
        nums.sort()
        l = len(nums)
        dp = nums.copy()
        for i in range(-2, -l - 1, -1):
            dp[i] += dp[i + 1]
        sm = dp[0]


        @cache
        def fn(n, s, i):
            if i == l:return False
            avg1 = (s / n) if n != 0 else 0
            avg2 = (sm - s) / (l - n)
            if avg1 > avg2:return False
            if avg1 == avg2:return True
            hold1 = (s + dp[i]) / (n + (l - i))
            hold2 = ((sm - s - dp[i]) / (i - n)) if (i - n) != 0 else 0
            if hold1 < hold2:return False
            return fn(n, s, i + 1) or fn(n + 1, s + nums[i], i + 1)
        
        broke = False       
        for i in range(1, len(nums)):
            if sm * i % len(nums) == 0:
                broke = True
                break
        if not broke:
            return False
        
        return fn(0, 0, 0)
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