CF86E.Long sequence

普及/提高-

通过率：0%

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题目描述

Input contains a single integer $k$ ( $2<=k<=50$ ).

输入格式

If there is no long sequence for a given $k$ , output "-1" (without quotes). Otherwise the first line of the output should contain $k$ integer numbers: $c_{1},c_{2},...,c_{k}$ (coefficients). The second line should contain first $k$ elements of the sequence: $a_{0},a_{1},...,a_{k-1}$ . All of them (elements and coefficients) should be equal to 0 or 1, and at least one $c_{i}$ has to be equal to 1.

If there are several solutions, output any.

输出格式

1. In the first sample: $c_{1}=1$ , $c_{2}=1$ , so $a_{n}=a_{n-1}+a_{n-2}\ (mod\ 2)$ . Thus the sequence will be:

so its period equals $3=2^{2}-1$ .

2. In the second sample: $c_{1}=0$ , $c_{2}=1$ , $c_{3}=1$ , so $a_{n}=a_{n-2}+a_{n-3}\ (mod\ 2)$ . Thus our sequence is:

and its period equals $7=2^{3}-1$ .

Periods are colored.

输入输出样例

输入#1
```
2
```
输出#1
```
1 1
1 0
```
输入#2
```
3
```
输出#2
```
0 1 1
1 1 1
```

说明/提示

1. In the first sample: $c_{1}=1$ , $c_{2}=1$ , so $a_{n}=a_{n-1}+a_{n-2}\ (mod\ 2)$ . Thus the sequence will be:

so its period equals $3=2^{2}-1$ .

2. In the second sample: $c_{1}=0$ , $c_{2}=1$ , $c_{3}=1$ , so $a_{n}=a_{n-2}+a_{n-3}\ (mod\ 2)$ . Thus our sequence is:

and its period equals $7=2^{3}-1$ .

Periods are colored.

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