Odd or Even

AtCoder

IDabc313_d

Time2000ms

Memory256MB

Difficulty—

This is an **interactive task** (where your program and the judge interact via Standard Input and Output). You are given an integer $N$ and an **odd number** $K$. The judge has a hidden length-$N$ sequence $A = (A_1, A_2, \dots, A_N)$ consisting of $0$ and $1$. While you cannot directly access the elements of sequence $A$, you are allowed to ask the judge the following query at most $N$ times. * Choose distinct integers $x_1, x_2, \dots$, and $x_K$ between $1$ and $N$, inclusive, to ask the parity of $A_{x_1} + A_{x_2} + \dots + A_{x_K}$. Determine $(A_1, A_2, \dots, A_N)$ by at most $N$ queries, and print the answer. Here, **the judge is adaptive**. In other words, the judge may modify the contents of $A$ as long as it is consistent with the responses to the past queries. Therefore, your program is considered correct if the output satisfies the following condition, and incorrect otherwise: * your program prints a sequence consistent with the responses to the queries so far, and that is the only such sequence. ## Constraints * $1 \leq K \lt N \leq 1000$ * $K$ is odd. * $A_i$ is $0$ or $1$. ## Input And Output This is an **interactive task** (where your program and the judge interact via Standard Input and Output). First of all, receive $N$ and $K$ from Standard Input. $N$ $K$ Then, repeat asking queries until you can uniquely determine $(A_1, A_2, \dots, A_N)$. Each query should be printed to Standard Output in the following format, where $x_1, x_2, \dots$, and $x_K$ are $K$ distinct integers between $1$ and $N$, inclusive. $?$ $x_1$ $x_2$ $\dots$ $x_K$ The response to the query is given from Standard Input in the following format. $T$ Here, $T$ denotes the response to the query. * $T$ is `0` when $A_{x_1} + A_{x_2} + \dots + A_{x_K}$ is even, and * $T$ is `1` when $A_{x_1} + A_{x_2} + \dots + A_{x_K}$ is odd. However, if $x_1, x_2, \dots$ and $x_K$ do not satisfy the constraints, or the number of queries exceeds $N$, then $T$ is `-1`. If the judge returns `-1`, your program is already considered incorrect, so terminate the program immediately. When you can determine all the elements of $A$, print those elements in the following format, and terminate the program immediately. $!$ $A_1$ $A_2$ $\dots$ $A_N$ [samples] ## Notes * **Print a newline and flush Standard Output at the end of each message. Otherwise, you may get a TLE verdict.** * **The verdict will be indeterminate if there is malformed output during the interaction or your program quits prematurely.** * Terminate the program immediately after printing the answer, or the verdict will be indeterminate. * The judge for this problem is adaptive. This means that the judge may modify the contents of $A$ as long as it is consistent with the responses to the past queries.

API Response (JSON)

{
  "problem": {
    "name": "Odd or Even",
    "description": {
      "content": "This is an **interactive task** (where your program and the judge interact via Standard Input and Output). You are given an integer $N$ and an **odd number** $K$.   The judge has a hidden length-$N$ s",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc313_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "This is an **interactive task** (where your program and the judge interact via Standard Input and Output).\nYou are given an integer $N$ and an **odd number** $K$.  \nThe judge has a hidden length-$N$ s...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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