CF1624F.Interacdive Problem

This problem is interactive.

We decided to play a game with you and guess the number $x$ ( $1 \le x < n$ ), where you know the number $n$ .

You can make queries like this:

• • c: this command assigns $x = x + c$ ( $1 \le c < n$ ) and then returns you the value $\lfloor\frac{x}{n}\rfloor$ ( $x$ divide by $n$ and round down).

You win if you guess the current number with no more than $10$ queries.

无

The interaction begins by reading an integer $n$ ( $2 < n \le 1000$ ), which is written in the input data on its own line.

Then you can make no more than $10$ queries. To make a query, print on a separate line:

• • c: this command will assign $x = x + c$ ( $1 \le c < n$ ) and then print $\lfloor\frac{x}{n}\rfloor$ (divide $x$ by $n$ and round down) on a separate line.

Print the answer, like the queries, on a separate line. The answer doesn't count in number of queries. To output it, use the following format:

• ! x: the current value of $x$ .

After that, your program should exit.

You have to use a flush operation right after printing each line. For example, in C++ you should use the function fflush(stdout), in Java — System.out.flush(), in Pascal — flush(output) and in Python — sys.stdout.flush().

Note that the interactor is not responsive.

To make a hack, use the following format: a single line must contain two numbers $x$ and $n$ , separated by a space.

In the first sample initially $x = 2$ . After the first query $x = 3$ , $\lfloor\frac{x}{n}\rfloor = 1$ .

In the second sample also initially $x = 2$ . After the first query $x = 3$ , $\lfloor\frac{x}{n}\rfloor = 0$ . After the second query $x = 4$ , $\lfloor\frac{x}{n}\rfloor = 0$ . After the third query $x=5$ , $\lfloor\frac{x}{n}\rfloor = 1$ .