[NEERC 2013] Interactive Interception

**这是一道交互题**。 平面上有一个点，初始位置 $x\in[0,p]$，速度 $q\in[0,v]$，其中 $p,v$ 是给定的。 你可以进行不超过 $100$ 次询问，形如 ``check L R``，满足 $0\le L\le R\le 10^9$，交互库会告诉你是否有 $x\in[L,R]$，每次询问之后，交互库会令 $x\gets x+q$。你需要在某个询问后确定此时的 $x$，并告诉交互库，格式形如 ``answer x``。 $1\le p,v\le 10^5$。

This is an interactive problem. North Eastern Emergency Rocket Control agency (NEERC) has developed a new radar control system that is designed to better control ballistic rocket interception. To test the new system NEERC agency had developed a mathematical model that is intended to show this system’s abilities. Let us represent a rocket as a point on a line. Initially the point is at some unknown integer location between $0$ and $p$, inclusive. It has some unknown speed of $q$ which is an integer between $0$ and $v$, inclusive. Each second the following happens. First, the control system makes a query to the radar of a form “`check L R`” and gets an answer whether the point is currently between $L$ and $R$, inclusive, or not. After that, the point’s coordinate increases by $q$. The goal of the radar control system is to learn the exact location of the point at the beginning of some second. When it does learn the point’s location, then instead of making a query to the radar, it gives a command to intercept the point at that location. You have to implement the control system that locates and intercepts the point while making at most $100$ queries to the radar. ### Interaction protocol Interaction starts with your program reading two integers — the values of $p$ and $v$ from the standard input($1\leq p\leq 10^5$,$1\leq v\leq 10^5$). After that your program must print commands to the standard output. Each command must be one of the following two. - “`check L R`” — make a query to the radar to get an answer whether the point is currently between $L$ and $R$, inclusive, or not. The answer must be read from the standard input and is either “`Yes`” or “`No`”. After that the point’s coordinate is increased by $q$. $L$ and $R$ must be integers. - “`answer x`” — the exact coordinate $x$ of the point is known, and you order to intercept the point. After printing this command your program must exit. Your program must write end-of-line sequence and flush the standard output after each command, including the last command “`answer x`” (end-of-line must be written and flushed before exiting).

2 2
Yes
No
Yes
Yes

check 1 3
check 3 5
check 2 4
check 4 5
answer 5

In the given example the point was initially at location $1$ and is moving at a speed $q = 1$.