Akash is interested in a new function F such that,
F(x) = GCD(1, x) + GCD(2, x) + ... + GCD(x, x)
where GCD is the Greatest Common Divisor.
Now, the problem is quite simple. Given an array A of size N, there are 2 types of queries:
1. C X Y : Compute the value of F( A[X] ) + F( A[X + 1] ) + F( A[X + 2] ) + .... + F( A[Y] ) (mod 10^9 + 7)
2. U X Y: Update the element of array A[X] = Y
Input:
First line of input contain integer N, size of the array.
Next line contain N space separated integers the elements of A.
Next line contain integer Q, number of queries.
Next Q lines contain one of the two queries.
Output:
For each of the first type of query, output the required sum (mod 10^9 + 7).
Constraints:
1 <= N <= 106
1 <= Q <= 105
1 <= Ai <= 5*105
For Update ,
1 <= X <= N
1 <= Y <= 5*105
For Compute ,
1 <= X <= Y <= N