<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 dp[300005][31];

bool get(int sf,int ss,int lf,int ls,vector<int> &v,int i){

       if(i>=v.size()){
           if(lf!=0&&ls!=0){
                  
              if(sf*ls==ss*lf)return true;
          }   
               return false;
       }
      
       if(dp[sf][lf]!=0&&(dp[sf][lf]&(1<<i))!=0)return false;//checking for the ith bit if the ith bit is 1 then return false
	   
       if(get(sf+v[i],ss,lf+1,ls,v,i+1))return true;
       if(get(sf,ss+v[i],lf,ls+1,v,i+1))return true;
	   
       dp[sf][lf]=(1<<i)|dp[sf][lf]; //set the ith bit to 1 which means if we are at ith index and we have sum=sf and length=lf then we cannot  split the array into two parts
       return false;
    }
	   bool splitArraySameAverage(vector<int>& v) {
        
        memset(dp,0,sizeof dp);
        
        return get(0,0,0,0,v,0);
}
};
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