This problem is interactive. We decided to play a game with you and guess the number xx (1≤x

Interacdive Problem solution codeforces

This problem is interactive.

We decided to play a game with you and guess the number xx (1x<n1≤x<n), where you know the number nn.

You can make queries like this:

  • + c: this command assigns x=x+cx=x+c (1c<n1≤c<n) and then returns you the value xn⌊xn⌋ (xx divide by nn and round down).

You win if you guess the current number with no more than 1010 queries.

Interaction Interacdive Problem solution codeforces

The interaction begins by reading an integer nn (2<n10002<n≤1000), which is written in the input data on its own line.

Then you can make no more than 1010 queries. To make a query, print on a separate line:

  • + c: this command will assign x=x+cx=x+c (1c<n1≤c<n) and then print xn⌊xn⌋ (divide xx by nn 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 xx.

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 xx and nn, separated by a space.

Examples Interacdive Problem solution codeforces
Copy
3

1

output

Copy
+ 1

! 3

input Interacdive Problem solution codeforces

Copy
5

0

0

1

output

Copy Interacdive Problem solution codeforces
+ 1

+ 1

+ 1

! 5

input Interacdive Problem solution codeforces

Copy
10

0

0

1

2

output

Copy Interacdive Problem solution codeforces
+ 2

+ 2

+ 3

+ 8

! 20
Note

In the first sample initially x=2x=2. After the first query x=3x=3xn=1⌊xn⌋=1.

In the second sample also initially x=2x=2. After the first query x=3x=3xn=0⌊xn⌋=0. After the second query x=4x=4xn=0⌊xn⌋=0. After the third query x=5x=5xn=1⌊xn⌋=1.

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