Please, another Queries on Array?

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Description:

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

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

"MULTIPLY l r x" — for every $$$i$$$ ($$$l \le i \le r$$$) multiply $$$a_i$$$ by $$$x$$$.
"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 of a positive integer $$$n$$$ (denoted as $$$\varphi(n)$$$) is the number of integers $$$x$$$ ($$$1 \le x \le n$$$) such that $$$\gcd(n,x) = 1$$$.

Input:

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.

"MULTIPLY l r x" ($$$1 \le l \le r \le n$$$, $$$1 \le x \le 300$$$) — denotes a multiplication query.
"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.

Output:

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

Sample Input:

4 4
5 9 1 2
TOTIENT 3 3
TOTIENT 3 4
MULTIPLY 4 4 3
TOTIENT 4 4

Sample Output:

1
1
2

Note:

In the first example, $$$\varphi(1) = 1$$$ for the first query, $$$\varphi(2) = 1$$$ for the second query and $$$\varphi(6) = 2$$$ for the third one.

Informação

Provedor Codeforces

Código CF1114F