<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 functools import cache
# class Solution:
#     def splitArraySameAverage(self, nums: List[int]) -> bool:
#         S_all = sum(nums)
#         c_all = len(nums)
#         n = len(nums)
#         @cache
#         def find(ind, c, S):
#             if (c == 0) and (S == 0):
#                 return True
#             if (ind == n) or (S < 0):
#                 return False
#             return find(ind + 1, n - 1, S - nums[ind]) or find(ind+1, n, S)
        
#         nums.sort(reverse = True)
#         for i in range(1, n//2 + 1):
#             if (i*S)%n != 0:
#                 if find(0, i, i*S//n):
#                     return True
#         return False
#             if (ind == n):
#                 return False
#             if (ind != 0) and (S != 0):
#                 if S * (c_all - c) == (S_all - S) * c:
#                     return True
#             return find(ind+1, c, S) or find(ind+1, c+1, S + nums[ind])
        
#         return find(0, 0, 0)
        
        
class Solution:
    def splitArraySameAverage(self, nums: List[int]) -> bool:
        @cache
        def canmake(idx, n, sm):
            if n == 0 and sm == 0: return True
            if idx == L or sm < 0: return False
            return canmake(idx+1, n-1, sm-nums[idx]) or canmake(idx+1, n, sm)    
        nums.sort(reverse = True)
        L = len(nums)
        sm = sum(nums)
        for n in range(1, L//2+1):
            if (n*sm)%L == 0 and canmake(0, n, n*sm/L): return True
        return False
        
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