<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 {
 public:
  bool splitArraySameAverage(vector<int>& nums) {
    int sum{0};

    for (int n : nums)
      sum += n;

    int n{static_cast<int>(nums.size())};
    int m{gcd(sum, n)};
    
    if (m == 1)
      return false;

    int r{n / m};
    int average{sum * r / n};
    int numMin{INT_MAX};

    for (int& i : nums) {
      i = i * r - average;
      numMin = min(numMin, i);
    }

    unordered_set<int> us;

    for (int i = 0; i < nums.size() - 1; i++) {
      if (!nums[i])
        return true;

      unordered_set<int> temp({nums[i]});

      for (int j : us) {
        if (!(nums[i] + j))
          return true;

        temp.insert(j);
        temp.insert(nums[i] + j);
      }

      us = temp;
    }

    return false;
  }

 private:
  int gcd(int a, int b) {
    if (!a)
      return b;

    if (!b)
      return a;

    

    while (a % b) {
      a %= b;
      swap(a, b);
    }

    return b;
  }
};
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