Two Lucky Numbers

AtCoder

IDarc131_a

Time2000ms

Memory256MB

Difficulty—

Mr. AtCoder reads in the newspaper that today's lucky number is a positive integer $A$ and tomorrow's is a positive integer $B$. Here, he defines a positive integer $x$ that satisfies both of the following conditions as a super-lucky number. * The decimal notation of $x$ contains $A$ as a contiguous substring. * The decimal notation of $2x$ contains $B$ as a contiguous substring. Actually, under the Constraints of this problem, there is always a super-lucky number less than $10^{18}$. Find one such number. ## Constraints * $1 \leq A < 10^8$ * $1 \leq B < 10^8$ * $A$ and $B$ have no leading `0`s. * All values in input are integers. ## Input Input is given from Standard Input in the following format: $A$ $B$ [samples]

Samples

Input #1

13
62

Output #1

131

One super-lucky number is $x = 131$, because:

*   $x = 131$ contains $13$ as a substring. ($1$\-st through $2$\-nd characters)
*   $2x = 262$ contains $62$ as a substring. ($2$\-nd through $3$\-rd characters)

Some other super-lucky numbers are $313$, $8135$, and $135797531$, which would also be accepted.

Input #2

69120
824

Output #2

869120

One super-lucky number is $x = 869120$, because:

*   $x = 869120$ contains $69120$ as a substring. ($2$\-nd through $6$\-th characters)
*   $2x = 1738240$ contains $824$ as a substring. ($4$\-th through $6$\-th characters)

The smallest super-lucky number is $69120$, but note that any lucky number with at most $18$ digits would be accepted.

Input #3

6283185
12566370

Output #3

6283185

When $x = 6283185$, $x$ is $A$ itself, and $2x$ is $B$ itself. In such a case too, $x$ is a super-lucky number.

API Response (JSON)

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    "name": "Two Lucky Numbers",
    "description": {
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      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc131_a"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Mr. AtCoder reads in the newspaper that today's lucky number is a positive integer $A$ and tomorrow's is a positive integer $B$.\nHere, he defines a positive integer $x$ that satisfies both of the foll...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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