Binary Multiplication#2178

Binary Multiplication

1 second
64 megabytes
Easy

We all know the rules of column multiplication. But can we write a program that performs this process for binary numbers? Let's try.

Input

Each test case contains two binary strings and separated by a space. The length of each string does not exceed . The input ends with the line .

Output

The output must be formatted as shown in the examples. You must also show the step-by-step procedure of the multiplication process. Different test cases should be separated by an empty line.

Examples

Example 1

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