<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:
    void formulate_Subsequences(vector<int>& nums, int i, int n, unordered_map<int, set<int>>& count, int sum, int numElements, int tot){
         if(numElements!=0){
            count[numElements].insert(sum*tot);
         }
         if(i==n) return;
         formulate_Subsequences(nums, i+1, n, count, sum+nums[i], numElements+1, tot);
         formulate_Subsequences(nums, i+1, n, count, sum, numElements, tot);
    }
    void printUnorderedMap(const unordered_map<int, set<int>>& umap) {
    for (const auto& pair : umap) {
        cout << "Key: " << pair.first << " -> Values: { ";
        for (const auto& value : pair.second) {
            cout << value << " ";
        }
        cout << "}\n";
    }
}
    bool splitArraySameAverage(vector<int>& nums) {
        int n = nums.size();
        int totalSum = accumulate(nums.begin(), nums.end(), 0);
        unordered_map<int, set<int>> countA, countB;
        formulate_Subsequences(nums, 0, n/2, countA, 0, 0, n);
        formulate_Subsequences(nums, n/2, n, countB, 0, 0, n);
        countB[0].insert(0);
        countA[0].insert(0);
        for(auto& pairA: countA){
            for(int ele:pairA.second){
                for(auto& pairB: countB){
                    int total_ele = pairA.first+pairB.first;
                    if(total_ele==n || total_ele==0) continue;
                    int req_sum = totalSum*total_ele-ele;
                    if(req_sum<0) continue;
                    auto it = pairB.second.lower_bound(req_sum);
                    if(it!=pairB.second.end() && (*it)==req_sum){return true;}
                }
            }
        }
        return false;
    }
};
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