{"raw_statement":[{"iden":"problem statement","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-$N$ sequence $A = (A_1, A_2, \\dots, A_N)$ consisting of $0$ and $1$.\nWhile you cannot directly access the elements of sequence $A$, you are allowed to ask the judge the following query at most $N$ times.\n\n*   Choose distinct integers $x_1, x_2, \\dots$, and $x_K$ between $1$ and $N$, inclusive, to ask the parity of $A_{x_1} + A_{x_2} + \\dots + A_{x_K}$.\n\nDetermine $(A_1, A_2, \\dots, A_N)$ by at most $N$ queries, and print the answer.  \nHere, **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.  \nTherefore, your program is considered correct if the output satisfies the following condition, and incorrect otherwise:\n\n*   your program prints a sequence consistent with the responses to the queries so far, and that is the only such sequence."},{"iden":"constraints","content":"*   $1 \\leq K \\lt N \\leq 1000$\n*   $K$ is odd.\n*   $A_i$ is $0$ or $1$."},{"iden":"input and output","content":"This is an **interactive task** (where your program and the judge interact via Standard Input and Output).\nFirst of all, receive $N$ and $K$ from Standard Input.\n\n$N$ $K$\n\nThen, repeat asking queries until you can uniquely determine $(A_1, A_2, \\dots, A_N)$.  \nEach 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.\n\n$?$ $x_1$ $x_2$ $\\dots$ $x_K$\n\nThe response to the query is given from Standard Input in the following format.\n\n$T$\n\nHere, $T$ denotes the response to the query.\n\n*   $T$ is `0` when $A_{x_1} + A_{x_2} + \\dots + A_{x_K}$ is even, and\n*   $T$ is `1` when $A_{x_1} + A_{x_2} + \\dots + A_{x_K}$ is odd.\n\nHowever, 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`.\nIf the judge returns `-1`, your program is already considered incorrect, so terminate the program immediately.\nWhen you can determine all the elements of $A$, print those elements in the following format, and terminate the program immediately.\n\n$!$ $A_1$ $A_2$ $\\dots$ $A_N$"},{"iden":"notes","content":"*   **Print a newline and flush Standard Output at the end of each message. Otherwise, you may get a TLE verdict.**\n*   **The verdict will be indeterminate if there is malformed output during the interaction or your program quits prematurely.**\n*   Terminate the program immediately after printing the answer, or the verdict will be indeterminate.\n*   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."},{"iden":"sample interaction","content":"In the following interaction, $N=5$ and $K=3$. **Note that the following output itself will result in WA.**  \nHere, $A = (1, 0, 1, 1, 0)$ is indeed consistent with the responses, but so is $(0, 0, 1, 0, 0)$, so sequence $A$ is not uniquely determined. Thus, this program is considered incorrect.\n\nInput\n\nOutput\n\nDescription\n\n`5 3`\n\nFirst, you are given integers $N$ and $K$.\n\n`? 2 4 1`\n\nYou ask a query with $(x_1, x_2, x_3) = (2, 4, 1)$.\n\n`0`\n\nThe response to the query is $0$, so the judge returns that value.\n\n`? 5 3 2`\n\nYou ask a query with $(x_1, x_2, x_3) = (5, 3, 2)$.\n\n`1`\n\nThe response to the query is $1$, so the judge returns that value.\n\n`! 1 0 1 1 0`\n\nYou print $(1, 0, 1, 1, 0)$ to guess $A$. Since sequence $A$ is not uniquely determined, the verdict will be WA."}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}