{"task": {"agent_timeout": 600, "task": "1325", "verifier_timeout": 7200, "instruction": "Please implement a Python 3 solution to the below problem.\nReason through the problem and:\n1. Restate the problem in plain English\n2. Conceptualize a solution first in plain English\n3. Write a pseudocode solution\n4. Save your solution as solution.py\nNo outside libraries are allowed.\n\n[BEGIN PROBLEM]\n\n**Note: The time limit for this problem is 4s, 2x the default.**\nTo celebrate the start of spring, Farmer John's $N$ cows ($1 \\leq N \\leq 2 \\cdot 10^5$) have invented an intriguing new dance, where they stand in a circle and re-order themselves in a predictable way.\n\nSpecifically, there are $N$ positions around the circle, numbered sequentially from $0$ to $N-1$, with position $0$ following position $N-1$.  A cow resides at each position.  The cows are also numbered sequentially from $0$ to $N-1$.  Initially, cow $i$ starts in position $i$.  You are told a set of $K$ positions $0=A_1<A_2< \\ldots< A_K<N$ that are \"active\", meaning the cows in these positions are the next to move ($1 \\leq K \\leq N$).  \n\nIn each minute of the dance, two things happen.  First, the cows in the active positions rotate: the cow at position $A_1$ moves to position $A_2$, the cow at position $A_2$ moves to position $A_3$, and so on, with the cow at position $A_K$ moving to position $A_1$.  All of these $K$ moves happen simultaneously, so the after the rotation is complete, all of the active positions still contain exactly one cow.  Next, the active positions themselves shift:\n$A_1$ becomes $A_1+1$, $A_2$ becomes $A_2+1$, and so on (if $A_i = N-1$ for some active position, then $A_i$ circles back around to $0$).\n\nPlease calculate the order of the cows after $T$ minutes of the dance ($1\\le T\\le 10^9$).\n\nINPUT FORMAT (input arrives from the terminal / stdin):\nThe first line contains three integers $N$, $K$, and $T$.\n\nThe second line contains $K$ integers representing the initial set of active positions\n$A_1,A_2, \\ldots A_K$.  Recall that $A_1 = 0$ and that these are given in increasing order.\n\nOUTPUT FORMAT (print output to the terminal / stdout):\nOutput the order of the cows after $T$ minutes, starting with the cow in position $0$, separated by\nspaces.\n\nSAMPLE INPUT:\n5 3 4\n0 2 3\nSAMPLE OUTPUT: \n1 2 3 4 0\n\nFor the example above, here are the cow orders and $A$ for the first four\ntimesteps:\n\n\nInitial, T = 0: order = [0 1 2 3 4], A = [0 2 3]\nT = 1: order = [3 1 0 2 4]\nT = 1: A = [1 3 4]\nT = 2: order = [3 4 0 1 2]\nT = 2: A = [2 4 0]\nT = 3: order = [2 4 3 1 0]\nT = 3: A = [3 0 1]\nT = 4: order = [1 2 3 4 0]\n\nSCORING:\nInputs 2-7: $N \\leq 1000, T \\leq 10000$Inputs 8-13: No additional constraints.\n\n\nProblem credits: Claire Zhang\n\n[END PROBLEM]\n", "memory": "2048m", "runnable": false, "difficulty": "medium", "language": "", "cpus": 1, "instruction_truncated": false, "category": "python_programming", "compose": false, "has_solution": true, "oracle": null, "docker_image": "", "taskset": "usaco", "tags": ["python", "programming", "usaco"]}, "runs": []}