Kaprekar Number

AtCoder

IDabc192_c

Time2000ms

Memory256MB

Difficulty—

For an integer $x$ not less than $0$, we define $g_1(x), g_2(x), f(x)$ as follows: * $g_1(x)=$ the integer obtained by rearranging the digits in the decimal notation of $x$ in descending order * $g_2(x)=$ the integer obtained by rearranging the digits in the decimal notation of $x$ in ascending order * $f(x)=g_1(x)-g_2(x)$ For example, we have $g_1(314)=431$, $g_2(3021)=123$, $f(271)=721-127=594$. Note that the leading zeros are ignored. Given integers $N, K$, find $a_K$ in the sequence defined by $a_0=N$, $a_{i+1}=f(a_i)\ (i\geq 0)$. ## Constraints * $0 \leq N \leq 10^9$ * $0 \leq K \leq 10^5$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $K$ [samples]

Samples

Input #1

314 2

Output #1

693

We have:

*   $a_0=314$
*   $a_1=f(314)=431-134=297$
*   $a_2=f(297)=972-279=693$

Input #2

1000000000 100

Output #2

0

We have:

*   $a_0=1000000000$
*   $a_1=f(1000000000)=1000000000-1=999999999$
*   $a_2=f(999999999)=999999999-999999999=0$
*   $a_3=f(0)=0-0=0$
*   $\vdots$

Input #3

6174 100000

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Kaprekar Number",
    "description": {
      "content": "For an integer $x$ not less than $0$, we define $g_1(x), g_2(x), f(x)$ as follows: *   $g_1(x)=$ the integer obtained by rearranging the digits in the decimal notation of $x$ in descending order *   ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc192_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "For an integer $x$ not less than $0$, we define $g_1(x), g_2(x), f(x)$ as follows:\n\n*   $g_1(x)=$ the integer obtained by rearranging the digits in the decimal notation of $x$ in descending order\n*   ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments