Binary Addition

You are given two non-negative integers a and b. Your task is to compute the sum s = a + b and output its binary representation without using any built-in binary conversion functions. The computation should be done by repeatedly dividing the sum by 2 and recording the remainders.

In mathematical terms, if s is the sum, then its binary representation is obtained by finding digits d_i such that:

$$ s = \sum_{i=0}^{k} d_i \times 2^i, \quad d_i \in \{0,1\} $$

and then arranging the digits in reverse order (from the last remainder to the first) to form the binary string.

inputFormat

The input consists of a single line containing two non-negative integers a and b separated by a space.

outputFormat

Output a single line which is the binary representation of the sum of the two integers.

3 5

1000