P17638 [ICPC 2019 Yinchuan R] Pot!!

Little Q is very sleepy, and he really needs some coffee to make him awake. At this time, Little L brings a pot to Little Q, and he states the pot as follows. For a prime number $p$, if $p^m \mid n$ and $p^{m+1} \nmid n$, we say $\text{pot}_p(n)=m$. The pot is very special that it can make everyone awake immediately. Now Little L provides $n~(1 \le n \le 10^5)$ integers $a_1, a_2, \cdots, a_n$ to Little Q, each of which is $1$ initially. After that, Little L shows $2$ types of queries: * **MULTIPLY l r x**: For every $i \in [l,r]$ ($1\le l\le r\le n$), multiply $a_i$ by $x$ ($2 \le x \le 10$). * **MAX l r**: Calculate the value of $$ \max_{l\le i\le r} \left\{ \max_{p|a_i} \left\{ \text{pot}_p (a_i) \right\} \right\}~(1 \le l \le r \le n), $$ where $p$ is prime. Now you need to perform $q~(1 \le q \le 10^5)$ queries of these two types of queries described above. If you perform a “**MULTIPLY**” query, you don't need to output anything. If you perform a “**MAX**” query, you need to output a line like `ANSWER y`, where $y$ the value you've calculated.

The first line contains two integers $n~(1 \le n \le 10^5)$ and $q~(1 \le q \le 10^5)$, the number of integers and the number of queries. Each of the next $q$ lines contains one type of query described above.

For each “**MAX**” query, output one line in the format of `ANSWER y`, where $y$ the value you have calculated.

If $m$ and $n$ are non-zero integers, or more generally, non-zero elements of an integral domain, it is said that $m$ divides $n$ if there exists an integer $k$, or an element $k$ of the integral domain, such that $m \times k=n$, and this is written as $m \mid n$.