Problem #1703 - ECNU Online Judge

单点时限: 2.0 sec

内存限制: 256 MB

Every positive integer $N$ can be written in at least one way as a sum of terms of the form $(2^{a}) (3^{b})$ where no term in the sum exactly divides any other term in the sum. For example:

$1 = (2^{0}) (3^{0})$ ,
$7 = (2^{2}) (3^{0}) + (2^{0}) (3^{1})$ ,
$31 = (2^{4}) (3^{0}) + (2^{0}) (3^{2}) + (2^{1}) (3^{1}) = (2^{2}) + (3^{3})$

Note from the example of $31$ that the representation is not unique.

Write a program which takes as input a positive integer $N$ and outputs a representation of $N$ as a sum of terms of the form $(2^{a}) (3^{b})$ .

输入格式

The first line of input contains a single integer $C$ ( $1 \leq C \leq 1000$ ) which is the number of datasets that follow.

Each dataset consists of a single line of input containing a single integer $N$ ( $1 \leq N < 2^{31}$ ), which is the number to be represented as a sum of terms of the form $(2^{a}) (3^{b})$ .

输出格式

For each dataset, the output will be a single line consisting of: The dataset number, a single space, the number of terms in your sum as a decimal integer followed by a single space followed by representations of the terms in the form x y with terms separated by a single space. x is the power of $2$ in the term and y is the power of $3$ in the term.

样例

Input

Output

1 1 0 0
2 2 0 1 2 0
3 2 0 3 2 0
4 1 5 5
5 1 0 12
6 8 0 16 2 15 3 13 4 12 7 8 9 6 10 5 15 2

4 人解决，13 人已尝试。

4 份提交通过，共有 50 份提交。

8.8 EMB 奖励。

创建: 17 年，7 月前.

修改: 7 年，3 月前.

最后提交: 1 年，8 月前.

来源: Greater New York 2006

1703. Non-divisible 2-3 Power Sums

输入格式

输出格式

样例

服务

开源

关于我们