Given two numbers arr1 and arr2 in base -2, return the result of adding them together.

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

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

 

Example 1:

Input: arr1 = [1,1,1,1,1], arr2 = [1,0,1]
Output: [1,0,0,0,0]
Explanation: arr1 represents 11, arr2 represents 5, the output represents 16.

Example 2:

Input: arr1 = [0], arr2 = [0]
Output: [0]

Example 3:

Input: arr1 = [0], arr2 = [1]
Output: [1]

 

Constraints:

• 1 <= arr1.length, arr2.length <= 1000
• arr1[i] and arr2[i] are 0 or 1
• arr1 and arr2 have no leading zeros