Broken Rounding

AtCoder

IDabc273_b

Time2000ms

Memory256MB

Difficulty—

Given a non-negative integer $X$, perform the following operation for $i=1,2,\dots,K$ in this order and find the resulting $X$. * Round $X$ off to the nearest $10^i$. * Formally, replace $X$ with $Y$ that is "the largest multiple of $10^i$ that minimizes $|Y-X|$." * Here are some examples: * Rounding $273$ off to the nearest $10^2$ yields $300$. * Rounding $999$ off to the nearest $10^3$ yields $1000$. * Rounding $100$ off to the nearest $10^{10}$ yields $0$. * Rounding $1015$ off to the nearest $10^1$ yields $1020$. ## Constraints * $X$ and $K$ are integers. * $0 \le X < 10^{15}$ * $1 \le K \le 15$ ## Input The input is given from Standard Input in the following format: $X$ $K$ [samples]

Samples

Input #1

2048 2

Output #1

2100

$X$ changes as $2048 \rightarrow 2050 \rightarrow 2100$ by the operations.

Input #2

1 15

Output #2

Input #3

999 3

Output #3

Input #4

314159265358979 12

Output #4

314000000000000

$X$ may not fit into a $32$\-bit integer type.

API Response (JSON)

{
  "problem": {
    "name": "Broken Rounding",
    "description": {
      "content": "Given a non-negative integer $X$, perform the following operation for $i=1,2,\\dots,K$ in this order and find the resulting $X$. *   Round $X$ off to the nearest $10^i$.     *   Formally, replace $X$ ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc273_b"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Given a non-negative integer $X$, perform the following operation for $i=1,2,\\dots,K$ in this order and find the resulting $X$.\n\n*   Round $X$ off to the nearest $10^i$.\n    *   Formally, replace $X$ ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments