Description

Teacher Mai finds that many problems about arithmetic function can be reduced to the following problem:

Maintain an array a with index from 1 to l. There are two kinds of operations:

1. Add v to ax for every x that gcd(x,n)=d.
2. Query Sigma(Xi) (i<=1<=X)

Format

Input

There are multiple test cases, terminated by a line "0 0".

For each test case, the first line contains two integers l,Q(1<=l,Q<=5*10^4), indicating the length of the array and the number of the operations.

In following Q lines, each line indicates an operation, and the format is "1 n d v" or "2 x" (1<=n,d,v<=2*10^5,1<=x<=l).

Output

For each case, output "Case #k:" first, where k is the case number counting from 1.

Then output the answer to each query.

Samples

6 4
1 4 1 2
2 5
1 3 3 3
2 3
0 0

Case #1:
6
7

Limitation