<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:

        n, total = len(nums), sum(nums)

        @cache
        def function(i,target,k):
            if k == 0:
                return target == 0

            if target<0 or i==len(nums) or k<0:
                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




        # mem={}
        # def func(idx, na,nb, sa,sb):
        #     if idx==len(nums):
        #         if na>0 and nb>0 and sa/na==sb/nb:
        #             return True
        #         else:
        #             return False
        #     if (idx,na,sa) in mem:
        #         return mem[(idx,na,sa)]
        #     if nb>na+1:
        #         return False
        #     mem[(idx+1,na+1,sa+nums[idx])]=func(idx+1, na+1,nb, sa+nums[idx], sb)
        #     mem[(idx+1,na, sa)]=func(idx+1, na,nb+1, sa, sb+nums[idx])
            
        #     return mem[(idx+1,na+1,sa+nums[idx])] or mem[(idx+1,na, sa)]
        # return func(0,0,0,0,0)




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