Problem Statement

This is a reactive problem.

The judge holds a hidden integer $X$ between $100$ and $10^5$, inclusive. By performing the following operation $1$ time, determine $X'$ after the operation.

1. You declare integers $A,B$ between $100$ and $10^5$, inclusive, and tell them to the judge.
2. Let $Y=A^B \mathrm{mod} (10^{9}+7)$.
3. The judge tells you $K=\gcd(X,Y)$.
4. $X'$ is set to $X^A \mathrm{mod} B$.

The judge is adaptive and may change the value of $X$ along the way, as long as it does not contradict its responses so far.

Constraints

• $100 \le X \le 10^5$

Input and Output

First, output $A,B$.

$A$ $B$

$K$ computed by the judge is given.

$K$

Output your guess of $X'$.

$X'$

An integer $\mathrm{ret}$ representing the result is given.

$\mathrm{ret}$

$\mathrm{ret}=1$ means that your guess is correct.
$\mathrm{ret}=0$ means that your guess is incorrect.

Notes

• The judge is adaptive. See the sample for a concrete example.
• Flush after every output.
  • For example, you can use std::cout<<std::endl in C++ or print(flush=True) in Python3.
• If your output format is incorrect, the judge result may be undefined.

Sample