Score : $300$ points

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 $1$.
• 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.

11

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:

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

0

0

576461302059761664

0
524288
549755813888
549756338176
576460752303423488
576460752303947776
576461302059237376
576461302059761664

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