问题 D: Change Matrix

There is an $n×n$ matrix where the element at the $i$\-th row and $j$\-th column is $\gcd(i,j)(1\le i,j\le n)$. There are $q$ operations, each time multiplying all the numbers in a row or a column by a number, and outputting the sum of all numbers in the current matrix, modulo $10^9+7$, ensuring that the operations are random.

The first line contains two positive integers $n$ and $q$ . The following $q$ lines, each line is one of the following two operations respectively representing that all numbers in the $x$\-th row or column need to be multiplied by $y$: \- R x y \- C x y

In the following $q$ lines, each line contains a single positive integer representing the answer.

$n,q \le 10^5,1 \le x \le n,0 \le y<10^9+7$ It is guaranteed that all operations are chosen independently and randomly from all valid operations with equal probability and there are at most $10$ test cases.