Alternating Power Ledger Sum

A retired mechanical adding machine at a currency-exchange counter stores every amount using a peculiar digit scheme instead of ordinary binary: each digit is 0 or 1, but the digit at position i counted from the right (0-indexed) contributes digit * (-2)^i to the value, rather than digit * 2^i. Because the place values alternate between positive and negative, the machine can represent both positive and negative amounts without ever needing a separate sign digit.

You are given two amounts already encoded this way, each written as a string of characters 0/1 from the most significant digit to the least significant digit, with no leading zero unless the encoded value is exactly 0 (in which case the string is exactly "0"). Compute the sum of the two encoded values and output it using the very same encoding: most significant digit first, and no leading zero unless the sum is exactly 0.

Input format

Line 1: a string A of characters 0/1. Line 2: a string B of characters 0/1.

Output format

A single line: the string encoding of A + B (as values), most significant digit first, with no leading zero unless the result is exactly "0".

Constraints

• 1 <= |A|, |B| <= 1000
• Every character of A and B is 0 or 1
• Neither A nor B has a leading zero unless it is exactly the single character 0

110
011

1

1
1

110