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
A[1] = 3, A[2] = 4, A[3] = 3
F(3) = GCD(1, 3) + GCD(2, 3) + GCD(3, 3) = 1 + 1 + 3 = 5.
F(4) = GCD(1, 4) + GCD(2, 4) + GCD(3, 4) + GCD(4, 4) = 1 + 2 + 1 + 4 = 8.
First query, the sum will be F(3) + F(4) = 5 + 8 = 13 (mod 10^9 + 7).
Second query, the sum will be F(3) + F(4) + F(3) = 5 + 8 + 5 = 18 (mod 10^9 + 7).
Third query, the sum will be F(3) = 5 (mod 10^9 + 7).
Fourth query will update A[1] = 4.
Fifth query, the sum will be F(4) + F(4) + F(3) = 8 + 8 + 5 = 21 (mod 10^9 + 7).
Sixth query, the sum will be F(4) + F(4) = 8 + 8 = 16 (mod 10^9 + 7).
