A12445. Please, another Queries on Array?
编程题
普及/提高-
知识点
题目描述
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 $\gcd(n,x) = 1$ .
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 $\gcd(n,x) = 1$ .
输入格式
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.
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.
输出格式
For each "TOTIENT" query, print the answer to it.
输入输出样例
输入 #1
4 4 5 9 1 2 TOTIENT 3 3 TOTIENT 3 4 MULTIPLY 4 4 3 TOTIENT 4 4
输出 #1
1 1 2
说明/提示
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.