Is Query Order

​This is a function implementation problem.

​A hidden integer $N$ satisfies $2 \leq N \leq 10^9$. You must identify $N$ by calling the ask() function at most $1\,000$ times.

​Function Implementation

​Your submission must include the header file order.h via #include "order.h". You must implement the following function:

int find()

• This function must return the hidden integer N.

​Within the find() function, you may call the following function:

int ask(long long a)

​

• $a$ must satisfy $1 \leq a \leq 9 \cdot 10^{18}$. If this condition is not met, you will receive a Wrong Answer verdict.
• The return values are as follows:
  • If $\gcd(a,N)=1$, it returns the order of $a$ modulo $N$. That is, it returns the smallest positive integer $r$ such that $a^r \equiv 1 \pmod N$.
  • If $\gcd(a,N)\neq 1$, it returns $0$.
• This function can be called at most $1\,000$ times within find(). If you exceed this limit, you will receive a Wrong Answer verdict.

​Your submitted code must not perform any input or output operations.