Alice and Bob communicate via a matrix channel. Alice wants to send a message to Bob. She has a bitstring representing her message and performs a bitwise encoding algorithm: She starts with the identity matrix</p>

[A =\begin{pmatrix} 1 & 0 \ 0 & 1 \end{pmatrix} ]

and then reads the bitstring starting from the left-most bit. For each 0-bit she multiplies the matrix (A) from the right with

[A = \begin{pmatrix} 1 & 0 \ 1 & 1 \end{pmatrix} \text{ , i.e. } A \leftarrow  A \cdot \begin{pmatrix} 1 & 0 \ 1 & 1 \end{pmatrix}  ]

For each 1-bit she multiplies the matrix (A) from the right with

[A = \begin{pmatrix} 1 & 1 \ 0 & 1 \end{pmatrix} \text{ , i.e. } A \leftarrow  A \cdot \begin{pmatrix} 1 & 1 \ 0 & 1 \end{pmatrix}  ]

Then the result is transmitted.

Now Bob accidentally deleted the software to decrypt a message from Alice. Can you help him to rewrite it?

입력 형식

The input consists of:</p>

• two lines, the (i)-th of them with two integers (a_{i1}) and (a_{i2}) (0 ≤ (a_{i1}), (a_{i2}) ≤ 2¹²⁸ − 1 for all 1 ≤ (i) ≤ 2), where [ \begin{pmatrix} a_{11} & a_{12} \ a_{21} & a_{22} \end{pmatrix} ]is the matrix containing the encoded message.

The bitstring representing the message consists of at most 120 characters.

출력 형식

Output the decoded bitstring.

예제 입력 1

2 1
3 2

예제 출력 1

010

예제 입력 2

18 29
13 21

예제 출력 2

10010101