Score : $300$ points

问题陈述

给定一个非负整数 $N$。按升序打印满足以下条件的所有非负整数 $x$。

• 在 $x$ 的二进制表示中包含数字 $1$ 的位置集合是 $N$ 的二进制表示中包含数字 $1$ 的位置集合的子集。
  • 即，对于每一个非负整数 $k$，下列条件成立：如果 $x$ 中在 "$2^k$" 位置上的数字为 $1$，那么 $N$ 中在 $2^k$ 位置上的数字也为 $1$。

以上为通义千问 qwen-max 翻译，仅供参考。

Problem Statement

You are given a non-negative integer $N$. Print all non-negative integers $x$ that satisfy the following condition in ascending order.

• The set of the digit positions containing $1$ in the binary representation of $x$ is a subset of the set of the digit positions containing $1$ in the binary representation of $N$.
  • That is, the following holds for every non-negative integer $k$: if the digit in the "$2^k$s" place of $x$ is $1$, the digit in the $2^k$s place of $N$ is $1$.

Constraints

• $N$ is an integer.
• $0 \le N < 2^{60}$
• In the binary representation of $N$, at most $15$ digit positions contain $1$.

Input

The input is given from Standard Input in the following format:

$N$

Output

Print the answer as decimal integers in ascending order, each in its own line.

Sample Input 1

11

Sample Output 1

0
1
2
3
8
9
10
11

The binary representation of $N = 11_{(10)}$ is $1011_{(2)}$.
The non-negative integers $x$ that satisfy the condition are:

• $0000_{(2)}=0_{(10)}$
• $0001_{(2)}=1_{(10)}$
• $0010_{(2)}=2_{(10)}$
• $0011_{(2)}=3_{(10)}$
• $1000_{(2)}=8_{(10)}$
• $1001_{(2)}=9_{(10)}$
• $1010_{(2)}=10_{(10)}$
• $1011_{(2)}=11_{(10)}$

Sample Input 2

0

Sample Output 2

0

Sample Input 3

576461302059761664

Sample Output 3

0
524288
549755813888
549756338176
576460752303423488
576460752303947776
576461302059237376
576461302059761664

The input may not fit into a $32$-bit signed integer.

update @ 2024/3/10 11:20:52