Many Balls

AtCoder

IDabc216_c

Time2000ms

Memory256MB

Difficulty—

We have an empty box. Takahashi can cast the following two spells any number of times in any order. * Spell $A$: puts one new ball into the box. * Spell $B$: doubles the number of balls in the box. Tell us a way to have exactly $N$ balls in the box with **at most $\mathbf{120}$ casts** of spells. It can be proved that there always exists such a way under the Constraints given. There is no way other than spells to alter the number of balls in the box. ## Constraints * $1 \leq N \leq 10^{18}$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ [samples]

Samples

Input #1

Output #1

AABA

This changes the number of balls as follows: $0 \xrightarrow{A} 1\xrightarrow{A} 2 \xrightarrow{B}4\xrightarrow{A} 5$.  
There are also other acceptable outputs, such as `AAAAA`.

Input #2

Output #2

BBABBAAAB

This changes the number of balls as follows: $0 \xrightarrow{B} 0 \xrightarrow{B} 0 \xrightarrow{A}1 \xrightarrow{B} 2 \xrightarrow{B} 4 \xrightarrow{A}5 \xrightarrow{A}6 \xrightarrow{A} 7 \xrightarrow{B}14$.  
It is not required to minimize the length of $S$.

API Response (JSON)

{
  "problem": {
    "name": "Many Balls",
    "description": {
      "content": "We have an empty box.   Takahashi can cast the following two spells any number of times in any order. *   Spell $A$: puts one new ball into the box. *   Spell $B$: doubles the number of balls in the ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc216_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "We have an empty box.  \nTakahashi can cast the following two spells any number of times in any order.\n\n*   Spell $A$: puts one new ball into the box.\n*   Spell $B$: doubles the number of balls in the ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments