Submask

AtCoder

IDabc269_c

Time2000ms

Memory256MB

Difficulty—

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: $N$ [samples]

Samples

Input #1

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:

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

Input #2

Output #2

Input #3

576461302059761664

Output #3

0
524288
549755813888
549756338176
576460752303423488
576460752303947776
576461302059237376
576461302059761664

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

API Response (JSON)

{
  "problem": {
    "name": "Submask",
    "description": {
      "content": "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 ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc269_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given a non-negative integer $N$. Print all non-negative integers $x$ that satisfy the following condition in ascending order.\n\n*   The set of the digit positions containing $1$ in the binary ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments