<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 isPossible(int m, int sum, int n) {
        for (int i = 1; i <= n; i++) {
            if ((sum * i) % n == 0) {
                return true;
            }
        }
        return false;
    }
    bool splitArraySameAverage(vector<int>& nums) {
        int n = nums.size();
        int m = n / 2;
        vector<unordered_set<int>> st(m + 1);
        int sum = 0;
        for (int& x : nums) {
            sum += x;
        }
        if (!isPossible(m, sum, n)) {
            return false;
        }

        st[0].insert(0);
        for (int& x : nums) {
            for (int i = m; i >= 1; i--) {
                for (const int& y : st[i - 1]) {
                    st[i].insert(y + x);
                }
            }
        }

        for (int i = 1; i <= m; ++i)
            if (sum * i % n == 0 && st[i].count(sum * i / n))
                return true;

        return false;
    }
};
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