A12445 | Please, another Queries on Array?

You are given an array $a_1, a_2, \ldots, a_n$ .

You need to perform $q$ queries of the following two types:

1. "MULTIPLY l r x" — for every $i$ ( $l \le i \le r$ ) multiply $a_i$ by $x$ .
2. "TOTIENT l r" — print $\varphi(\prod \limits_{i=l}^{r} a_i)$ taken modulo $10^9+7$ , where $\varphi$ denotes Euler's totient function.

The [Euler's totient function](http://gg.gg/euler_totient) of a positive integer $n$ (denoted as $\varphi(n)$ ) is the number of integers $x$ ( $1 \le x \le n$ ) such that $\gcd(n,x) = 1$ .

The first line contains two integers $n$ and $q$ ( $1 \le n \le 4 \cdot 10^5$ , $1 \le q \le 2 \cdot 10^5$ ) — the number of elements in array $a$ and the number of queries.

The second line contains $n$ integers $a_1, a_2, \ldots, a_n$ ( $1 \le a_i \le 300$ ) — the elements of array $a$ .

Then $q$ lines follow, describing queries in the format given in the statement.

1. "MULTIPLY l r x" ( $1 \le l \le r \le n$ , $1 \le x \le 300$ ) — denotes a multiplication query.
2. "TOTIENT l r" ( $1 \le l \le r \le n$ ) — denotes a query on the value of Euler's totient function.

It is guaranteed that there is at least one "TOTIENT" query.

For each "TOTIENT" query, print the answer to it.