16 人解决，18 人已尝试。
22 份提交通过，共有 34 份提交。
3.8 EMB 奖励。
单点时限: 2.0 sec
内存限制: 256 MB
An addition chain for $n$ is an integer sequence ${a_0, a_1,a_2,\ldots,a_m}$ with the following four properties:
You are given an integer $n$. Your job is to construct an addition chain for $n$ with minimal length. If there is more than one such sequence, any one is acceptable.
For example, ${1, 2, 3, 5}$ and ${1, 2, 4, 5}$ are both valid solutions when you are asked for an addition chain for $5$.
The input will contain one or more test cases. Each test case consists of one line containing one integer $n$ ($1 \le n \le 100$). Input is terminated by a value of zero (0) for $n$.
For each test case, print one line containing the required integer sequence. Separate the numbers by one blank.
5 7 12 15 77 0
1 2 4 5 1 2 4 6 7 1 2 4 8 12 1 2 4 5 10 15 1 2 4 8 9 17 34 68 77
16 人解决，18 人已尝试。
22 份提交通过，共有 34 份提交。
3.8 EMB 奖励。