---{"category_name":"easy","problem_code":"ONESGUESS","problem_name":"Ones Guessing","problemComponents":{"constraints":"- $1 \\leq N \\leq 5000$\n- All characters of $S$ are $\\texttt{0}$ or $\\texttt{1}$.\n- $1 \\leq K \\leq N$\n","constraintsState":true,"subtasks":"- 30 points : $1 \\leq R \\leq 10000$\n- 70 points : $1 \\leq R \\leq 10^9$\n","subtasksState":false,"inputFormat":"- Begin by reading a line containing a single integer $N$. Afterwards, you should make **exactly** $N$ guesses.\n- To make the $i$-th guess ($1 \\leq i \\leq N$), you should output a single integer $G_i$ ($1 \\leq G_i \\leq N$). In response, you should read in a single character — the $i$-th character of $S$.\n- After exactly $N$ guesses, your program should exit the interaction protocol. Otherwise, you may receive any verdict.\n\nAfter printing a guess, do not forget to output the end of line and flush the output.\n\nThe interactor is **adaptive**. That is, the string $S$ is not fixed before the interaction and can change depending on your guesses.","inputFormatState":true,"outputFormat":"","outputFormatState":false,"sampleTestCases":{"0":{"id":1,"input":"5\n0\n1\n0\n1\n0\n","output":"5\n4\n2\n2\n3","explanation":"In the example $N=5$ and $S = \\texttt{01010}$, so $K=2$. The interaction proceeds as follows.\n\n$$\n\\begin{array}{ccc} \ni \u0026amp; \\text{Guess (contestant)} \u0026amp; \\text{Response (interactor)} \\\\\n1 \u0026amp; 5 \u0026amp; \\texttt{0} \\\\\n2 \u0026amp; 4 \u0026amp; \\texttt{1} \\\\\n3 \u0026amp; 2 \u0026amp; \\texttt{0} \\\\\n4 \u0026amp; 2 \u0026amp; \\texttt{1} \\\\\n5 \u0026amp; 3 \u0026amp; \\texttt{0} \\\\\n\\end{array}\n$$\n\nThe contestant wins, since $G_4=K$ and $S_4=\\texttt{1}$. Note that although the contestant won before all $N$ guesses, the programs are required to interact for all $N$ guesses. Also note that the contestant doesn\u0027t win at $i=3$, since $S_3 \\neq \\texttt{1}$ (even though $K$ is guessed correctly).","isDeleted":false}}},"video_editorial_url":"","languages_supported":{"0":"CPP14","1":"C","2":"JAVA","3":"PYTH 3.6","4":"CPP17","5":"PYTH","6":"PYP3","7":"CS2","8":"ADA","9":"PYPY","10":"TEXT","11":"PAS fpc","12":"NODEJS","13":"RUBY","14":"PHP","15":"GO","16":"HASK","17":"TCL","18":"PERL","19":"SCALA","20":"LUA","21":"kotlin","22":"BASH","23":"JS","24":"LISP sbcl","25":"rust","26":"PAS gpc","27":"BF","28":"CLOJ","29":"R","30":"D","31":"CAML","32":"FORT","33":"ASM","34":"swift","35":"FS","36":"WSPC","37":"LISP clisp","38":"SQL","39":"SCM guile","40":"PERL6","41":"ERL","42":"CLPS","43":"ICK","44":"NICE","45":"PRLG","46":"ICON","47":"COB","48":"SCM chicken","49":"PIKE","50":"SCM qobi","51":"ST","52":"SQLQ","53":"NEM"},"max_timelimit":1,"source_sizelimit":50000,"problem_author":"flamestorm153","problem_tester":"","date_added":"4-01-2022","tags":{"0":"easy","1":"flamestorm153","2":"snckfl21","3":"snckfp21"},"problem_difficulty_level":"Unavailable","best_tag":"","editorial_url":"https://discuss.codechef.com/problems/ONESGUESS","time":{"view_start_date":1641747600,"submit_start_date":1641747600,"visible_start_date":1641747600,"end_date":1735669800},"is_direct_submittable":false,"problemDiscussURL":"https://discuss.codechef.com/search?q=ONESGUESS","is_proctored":false,"visitedContests":{},"layout":"problem"}---This is an example statement in markdown. This is the statement of the problem [TANDC](https://codechef.com/problems/TANDC) on CodeChef. The main statement starts with the next paragraph. Please make sure to remove this paragraph from your statement before publishing your problem. If your problem doesn't contain Subtasks, you should remove the section subtask too. We are using markdown the syntax of which can be seen [at](https://github.com/showdownjs/showdown/wiki/Showdown's-Markdown-syntax). We request you to not use any HTML tags in the statement, e.g. no p, ul, li, pre, br or b tags. If you face any issue, please contact admins or email us at help@codechef.com.Tracy is teaching Charlie maths via a game called $N$-Cube, which involves three sections involving $N$.Tracy gives Charlie a number $N$, and Charlie makes a list of $N$-th powers of integers in increasing order $1^N, 2^N, 3^N, \dot, \text{so on}$. This teaches him exponentiation.Then Charlie performs the following subtraction game $N$ times: Take all pairs of consecutive numbers in the list and take their difference. These differences then form the new list for the next iteration of the game. Eg, if $N$ was 6, the list proceeds as $[1, 64, 729, 4096 ... ]$ to $[63, 685, 3367 ...]$, and so on $5$ more times.After the subtraction game, Charlie has to correctly tell Tracy the $N$-th element of the list. This number is the *value of the game*.After practice Charlie became an expert in the game. To challenge him more, Tracy will give two numbers $M$ (where $M$ is a prime) and $R$ instead of just a single number $N$, and the game must start from $M_R - 1$ instead of $N$. Since the *value of the game* can now become large, Charlie just have to tell the largest integer $K$ such that $M_K$ divides this number. Since even $K$ can be large, output $K$ modulo 1000000007 ($10^9 + 7$).<aside style='background: #f8f8f8;padding: 10px 15px;'><div>All submissions for this problem are available.</div></aside>