Algorithms and Data Structures

Multiply Binary Numbers

You are given two binary numbers represented as strings and . Your task is to calculate the product of these two binary numbers and output the result in binary form.

Input

The first line contains the first binary string ().

The second line contains the second binary string ().

Output

Output a single string representing the product of and in binary form.

Examples

Input

Output

1101 101

1000001

1011 101

110111

Constraints

Time limit: 2 seconds

Memory limit: 512 MB

Output limit: 1 MB

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