<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:
   int n;

vector<vector<vector<bool>>>dp;

bool is_posibble(int idx, int el, int sum, vector<int>& nums){
    
    if(el == 0)
    {
        return sum == 0;
    }
    
    if(idx == n) 
    {
        return false;
    }
    if(sum < 0)
    {
        return false;
    }
    if(dp[idx][el][sum] == false )
    {
        return false;
    }
    
    if(is_posibble(idx + 1, el - 1, sum - nums[idx],nums))
    {
        return dp[idx][el][sum] = true;
    }
    if(is_posibble(idx + 1, el, sum, nums))
    {
        return dp[idx][el][sum] = true;
    }
    
    return dp[idx][el][sum] = false;
}

bool splitArraySameAverage(vector<int>& nums) {
    
    n = nums.size();
    
    int sum = accumulate(nums.begin(), nums.end(), 0);
    
    dp.resize(n, vector<vector<bool>>(n, vector<bool>(sum + 1, true)));
    
    for(int i = 1; i <= n-1; i++){
        
        if((sum * i) % n == 0){
            
            int curr_sum = (sum * i)/n;
            
            if(is_posibble(0, i, curr_sum, nums)){
                
                return true;
            }
            
        }
        
    }
    
    return false;
}
};
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