<p>Given two numbers <code>arr1</code> and <code>arr2</code> in base <strong>-2</strong>, return the result of adding them together.</p>

<p>Each number is given in <em>array format</em>:&nbsp; as an array of 0s and 1s, from most significant bit to least significant bit.&nbsp; For example, <code>arr = [1,1,0,1]</code> represents the number <code>(-2)^3&nbsp;+ (-2)^2 + (-2)^0 = -3</code>.&nbsp; A number <code>arr</code> in <em>array, format</em> is also guaranteed to have no leading zeros: either&nbsp;<code>arr == [0]</code> or <code>arr[0] == 1</code>.</p>

<p>Return the result of adding <code>arr1</code> and <code>arr2</code> in the same format: as an array of 0s and 1s with no leading zeros.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> arr1 = [1,1,1,1,1], arr2 = [1,0,1]
<strong>Output:</strong> [1,0,0,0,0]
<strong>Explanation: </strong>arr1 represents 11, arr2 represents 5, the output represents 16.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> arr1 = [0], arr2 = [0]
<strong>Output:</strong> [0]
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> arr1 = [0], arr2 = [1]
<strong>Output:</strong> [1]
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= arr1.length,&nbsp;arr2.length &lt;= 1000</code></li>
	<li><code>arr1[i]</code>&nbsp;and <code>arr2[i]</code> are&nbsp;<code>0</code> or <code>1</code></li>
	<li><code>arr1</code> and <code>arr2</code> have no leading zeros</li>
</ul>

class Solution {
public:
   vector<int> addNegabinary(vector<int>& arr1, vector<int>& arr2) {
        vector<int> ans;
        int l= max(arr1.size(),arr2.size())+2;    // carry can be forwarded to maximum 2 positions. 
        int a1,a2,sum, carry=0,r;
        reverse(arr1.begin(),arr1.end());
        reverse(arr2.begin(),arr2.end());
        int i=0; 
        
        while(i<l){
            a1 = i<arr1.size() ? arr1[i] : 0;
            a2 = i<arr2.size() ? arr2[i] : 0; 
            sum = a1+a2+carry;
            r= sum%(-2);
            carry= sum/ (-2);
            if(r<0){
                r+=abs(-2);
                carry =carry+1;
            }
            ans.push_back(r);
            i++;
        }
        while(ans.back()==0&&ans.size()!=1)
            ans.pop_back();     // remove trailing zeroes 
        reverse(ans.begin(),ans.end());
        
        return ans;
    }
};
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