Rocket

题意翻译

这是一道交互题，嘿嘿。 现在有一个人坐着火箭去火星。他飞啊飞啊好无聊的。所以他想知道到从出发地到火星有多远，这是一个距离$x$，$x$在$[1,m]$这个范围内，但是他就是不知道$x$。 他就去问这个火箭，告诉火箭一个$y$，如果$x<y$火箭就会告诉你-1，如果$x=y$火箭就会告诉你0，如果$x>y$火箭会告诉你1。 但是问题来了，这个火箭定期抽抽风，抽风的周期是一个$n$，这个周期可以被表述成一个长度为$n$的01序列，1代表正常回答，0代表抽风。抽风时火箭的回答本应是正确的$t$，但是因为抽风就变成了$-t$。 现在给你$n,m$，和至多$60$的询问，希望你通过询问得到$x$，数据范围$ans[1,1e9]$ $n[1,30]$。 除$m,n$的输入外，你需要在询问的回答前加上**fflush(stdout);**语句(c++)，其他语言见原题面。 **请谨记，询问的输出必须换行**

题目描述

This is an interactive problem. Natasha is going to fly to Mars. Finally, Natasha sat in the rocket. She flies, flies... but gets bored. She wishes to arrive to Mars already! So she decides to find something to occupy herself. She couldn't think of anything better to do than to calculate the distance to the red planet. Let's define $ x $ as the distance to Mars. Unfortunately, Natasha does not know $ x $ . But it is known that $ 1 \le x \le m $ , where Natasha knows the number $ m $ . Besides, $ x $ and $ m $ are positive integers. Natasha can ask the rocket questions. Every question is an integer $ y $ ( $ 1 \le y \le m $ ). The correct answer to the question is $ -1 $ , if $ x<y $ , $ 0 $ , if $ x=y $ , and $ 1 $ , if $ x>y $ . But the rocket is broken — it does not always answer correctly. Precisely: let the correct answer to the current question be equal to $ t $ , then, if the rocket answers this question correctly, then it will answer $ t $ , otherwise it will answer $ -t $ . In addition, the rocket has a sequence $ p $ of length $ n $ . Each element of the sequence is either $ 0 $ or $ 1 $ . The rocket processes this sequence in the cyclic order, that is $ 1 $ -st element, $ 2 $ -nd, $ 3 $ -rd, $ \ldots $ , $ (n-1) $ -th, $ n $ -th, $ 1 $ -st, $ 2 $ -nd, $ 3 $ -rd, $ \ldots $ , $ (n-1) $ -th, $ n $ -th, $ \ldots $ . If the current element is $ 1 $ , the rocket answers correctly, if $ 0 $ — lies. Natasha doesn't know the sequence $ p $ , but she knows its length — $ n $ . You can ask the rocket no more than $ 60 $ questions. Help Natasha find the distance to Mars. Assume, that the distance to Mars does not change while Natasha is asking questions. Your solution will not be accepted, if it does not receive an answer $ 0 $ from the rocket (even if the distance to Mars is uniquely determined by the already received rocket's answers).

输入输出格式

输入格式

The first line contains two integers $ m $ and $ n $ ( $ 1 \le m \le 10^9 $ , $ 1 \le n \le 30 $ ) — the maximum distance to Mars and the number of elements in the sequence $ p $ .

输出格式

You can ask the rocket no more than $ 60 $ questions. To ask a question, print a number $ y $ ( $ 1\le y\le m $ ) and an end-of-line character, then do the operation flush and read the answer to the question. If the program reads $ 0 $ , then the distance is correct and you must immediately terminate the program (for example, by calling exit(0)). If you ignore this, you can get any verdict, since your program will continue to read from the closed input stream. If at some point your program reads $ -2 $ as an answer, it must immediately end (for example, by calling exit(0)). You will receive the "Wrong answer" verdict, and this will mean that the request is incorrect or the number of requests exceeds $ 60 $ . If you ignore this, you can get any verdict, since your program will continue to read from the closed input stream. If your program's request is not a valid integer between $ -2^{31} $ and $ 2^{31}-1 $ (inclusive) without leading zeros, then you can get any verdict. You can get "Idleness limit exceeded" if you don't print anything or if you forget to flush the output. To flush the output buffer you can use (after printing a query and end-of-line): - fflush(stdout) in C++; - System.out.flush() in Java; - stdout.flush() in Python; - flush(output) in Pascal; - See the documentation for other languages. Hacking Use the following format for hacking: In the first line, print $ 3 $ integers $ m,n,x $ ( $ 1\le x\le m\le 10^9 $ , $ 1\le n\le 30 $ ) — the maximum distance to Mars, the number of elements in the sequence $ p $ and the current distance to Mars. In the second line, enter $ n $ numbers, each of which is equal to $ 0 $ or $ 1 $ — sequence $ p $ . The hacked solution will not have access to the number $ x $ and sequence $ p $ .

输入输出样例

输入样例 #1

5 2
1
-1
-1
1
0

输出样例 #1

1
2
4
5
3

说明

In the example, hacking would look like this: 5 2 3 1 0 This means that the current distance to Mars is equal to $ 3 $ , Natasha knows that it does not exceed $ 5 $ , and the rocket answers in order: correctly, incorrectly, correctly, incorrectly ... Really: on the first query ( $ 1 $ ) the correct answer is $ 1 $ , the rocket answered correctly: $ 1 $ ; on the second query ( $ 2 $ ) the correct answer is $ 1 $ , the rocket answered incorrectly: $ -1 $ ; on the third query ( $ 4 $ ) the correct answer is $ -1 $ , the rocket answered correctly: $ -1 $ ; on the fourth query ( $ 5 $ ) the correct answer is $ -1 $ , the rocket answered incorrectly: $ 1 $ ; on the fifth query ( $ 3 $ ) the correct and incorrect answer is $ 0 $ .

题意翻译

这是一道交互题，嘿嘿。 现在有一个人坐着火箭去火星。他飞啊飞啊好无聊的。所以他想知道到从出发地到火星有多远，这是一个距离$x$，$x$在$[1,m]$这个范围内，但是他就是不知道$x$。 他就去问这个火箭，告诉火箭一个$y$，如果$x<y$火箭就会告诉你-1，如果$x=y$火箭就会告诉你0，如果$x>y$火箭会告诉你1。 但是问题来了，这个火箭定期抽抽风，抽风的周期是一个$n$，这个周期可以被表述成一个长度为$n$的01序列，1代表正常回答，0代表抽风。抽风时火箭的回答本应是正确的$t$，但是因为抽风就变成了$-t$。 现在给你$n,m$，和至多$60$的询问，希望你通过询问得到$x$，数据范围$ans[1,1e9]$ $n[1,30]$。 除$m,n$的输入外，你需要在询问的回答前加上**fflush(stdout);**语句(c++)，其他语言见原题面。 **请谨记，询问的输出必须换行**