In a galaxy far, far away, there are two integer sequence a and b of length n.
b is a static permutation of 1 to n. Initially a is filled with zeroes.
There are two kind of operations:
1. add l r: add one for $a_l,a_{l+1}...a_r$
2. query l r: query $\sum_{i=l}^r \lfloor a_i / b_i \rfloor$

There are multiple test cases, please read till the end of input file.
For each test case, in the first line, two integers n,q, representing the length of a,b and the number of queries.
In the second line, n integers separated by spaces, representing permutation b.
In the following q lines, each line is either in the form 'add l r' or 'query l r', representing an operation.
$1 \leq n,q \leq 100000$, $1 \leq l \leq r \leq n$, there're no more than 5 test cases.

Output the answer for each 'query', each one line.