<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 {
    unordered_map<string,bool> m;
public:
    bool splitArraySameAverage(vector<int>& nums) {
        int n = nums.size();
        int sum = accumulate(nums.begin(),nums.end(),0);

        
        for(int i=1;i<=n-1;i++){
            if((sum * i) % n == 0){
                int reqdSum = sum * i;
                reqdSum /= n;
                
                // vector<vector<vector<int>>> dp(reqdSum+1,vector<vector<int>>(i+1,vector<int>(n+1,-1)));
                
                if(help(nums,reqdSum,i,0))
                    return true;
            }
        }

        return false;
    }

    bool help(vector<int>& nums,int sum,int count,int idx){
        if(count == 0) return (sum == 0);
        if(idx == nums.size()) return false;

        string key = to_string(sum) + to_string(count) + to_string(idx);
        if(m.find(key) != m.end()) return m[key];

        if(nums[idx] <= sum){
            if(help(nums,sum-nums[idx],count-1,idx+1))
                return m[key] = true;
        }

        if(help(nums,sum,count,idx+1))
            return m[key] = true;

        return m[key] = false;
    }
};
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