This is an interactive problem.

Kira has a hidden positive integer $n$, and Hayato needs to guess it.

Initially, Kira gives Hayato the value $\mathrm{cnt}$ — the number of unit bits in the binary notation of $n$. To guess $n$, Hayato can only do operations of one kind: choose an integer $x$ and subtract it from $n$. Note that after each operation, the number $n$ changes. Kira doesn't like bad requests, so if Hayato tries to subtract a number $x$ greater than $n$, he will lose to Kira. After each operation, Kira gives Hayato the updated value $\mathrm{cnt}$ — the number of unit bits in the binary notation of the updated value of $n$.

Kira doesn't have much patience, so Hayato must guess the original value of $n$ after no more than $30$ operations.

Since Hayato is in elementary school, he asks for your help. Write a program that guesses the number $n$. Kira is an honest person, so he chooses the initial number $n$ before all operations and does not change it afterward.

Interaction

To guess $n$, you can perform the operation at most $30$ times. To do that, print a line with the following format: "- x" ($1 \le x \le 10^9$).

After this operation, the number $x$ is subtracted from $n$, and therefore $n$ is changed. If the number $x$ is greater than the current value of $n$, then the request is considered invalid.

After the operation read a line containing a single non-negative integer $\mathrm{cnt}$ — the number of unit bits in the binary notation of the current $n$ after the operation.

When you know the initial value of $n$, print one line in the following format: "! n" ($1 \le n \le 10^9$).

After that, move on to the next test case, or terminate the program if there are none.

If your program performs more than $30$ operations for one test case, subtracts a number $x$ greater than $n$, or makes an incorrect request, then response to the request will be -1, after receiving such response, your program must exit immediately to receive the Wrong Answer verdict. Otherwise, you can get any other verdict.

After printing a query or the answer, do not forget to output the end of line and flush the output. Otherwise, you will get Idleness limit exceeded. To do this, use:

• fflush(stdout) or cout.flush() in C++;
• System.out.flush() in Java;
• flush(output) in Pascal;
• stdout.flush() in Python;
• see documentation for other languages.

Hacks

To make a hack, use the following format.

The first line should contain a single integer $t$ ($1 \leq t \leq 500$).

Each test case should contain one integer $n$ ($1 \leq n \leq 10^9$) on a separate line.